docs(harnesses): second polish pass on multi-harness pages

- Fix link-text/URL mismatch in harnesses overview: link reads 'triggers'
  but pointed to /integrations/; repoint to /triggers/.
- Add Oxford comma to 'environment compute, triggers, and observability'
  in three places (style guide requires the serial comma).
- Match the actual UI label: 'the harness dropdown' -> 'the **Agent harness**
  dropdown' on the Claude Code, Codex, and Warp Agent cloud pages
  (confirmed via harness_selector.rs).
- Unify product descriptors so the auth page matches the harness pages:
  Claude Code is now 'Anthropic's agentic coding tool' and Codex is
  'OpenAI's coding agent'.
- 'Key icon above the input box' -> 'key icon above the input' (the spec
  uses lowercase 'key icon' and the rest of the docs say 'above the input').
- Drop redundant article: 'the same toolbelt the Warp Agent uses locally'
  -> '...the same toolbelt Warp Agent uses locally'.
- Drop redundant qualifier: 'Warp Agent with Oz is the same agent runtime'
  -> 'Warp Agent is the same agent runtime' (page context already
  establishes Oz).
- Disambiguate 'Claude Code and Codex call Anthropic or OpenAI directly'
  -> '...each call their provider directly' so it's clear each harness
  calls its own provider.

Co-Authored-By: Oz <oz-agent@warp.dev>

Author: oz-agent

src/content/docs/agent-platform/cloud-agents/harnesses/authentication.mdx

@@ -17,7 +17,7 @@ Auth secrets can be scoped to a **team** (available to all teammates' runs) or *
 
 ## Connecting Claude Code credentials
 
-Claude Code is Anthropic's coding agent. For more on Claude Code authentication, see [Anthropic's Claude Code auth docs](https://code.claude.com/docs/en/authentication).
+Claude Code is Anthropic's agentic coding tool. For more on Claude Code authentication, see [Anthropic's Claude Code auth docs](https://code.claude.com/docs/en/authentication).
 
 ### Create an Anthropic API key
 
@@ -31,7 +31,7 @@ Oz also supports Bedrock-routed credentials (**Anthropic Bedrock API key** and *
 
 #### Warp desktop app
 
-In Cloud Mode, click the Key icon above the input box and add your Anthropic credential.
+In Cloud Mode, click the key icon above the input and add your Anthropic credential.
 
 #### Oz web app
 
@@ -49,7 +49,7 @@ Add `--description "..."` to record rotation notes or owner info. Replace `--tea
 
 ## Connecting Codex credentials
 
-Codex is OpenAI's CLI coding agent. For more on Codex authentication, see [OpenAI's Codex auth docs](https://developers.openai.com/codex/auth).
+Codex is OpenAI's coding agent. For more on Codex authentication, see [OpenAI's Codex auth docs](https://developers.openai.com/codex/auth).
 
 :::caution
 A ChatGPT subscription (Plus, Pro, Team) does not include API access. You need a separate OpenAI API key with API credits.
@@ -65,7 +65,7 @@ A ChatGPT subscription (Plus, Pro, Team) does not include API access. You need a
 
 #### Warp desktop app
 
-In Cloud Mode, click the Key icon above the input box and add your OpenAI credential.
+In Cloud Mode, click the key icon above the input and add your OpenAI credential.
 
 #### Oz web app
 

src/content/docs/agent-platform/cloud-agents/harnesses/claude-code.mdx

@@ -36,13 +36,13 @@ Claude Code calls Anthropic directly using credentials your team provides. Oz su
 * **Anthropic Bedrock API key** - For Bedrock-routed inference using an API key.
 * **Anthropic Bedrock access key** - For Bedrock-routed inference using AWS access credentials.
 
-Anthropic bills your account directly for inference. Warp credits cover the rest of the platform — environment compute, triggers, observability.
+Anthropic bills your account directly for inference. Warp credits cover the rest of the platform — environment compute, triggers, and observability.
 
 For setup steps, see [Connecting Claude Code credentials](/agent-platform/cloud-agents/harnesses/authentication/#connecting-claude-code-credentials).
 
 ## Starting a Claude Code run
 
-* **Warp app** - In Cloud Mode, click the harness dropdown above the input and choose **Claude Code**.
+* **Warp app** - In Cloud Mode, click the **Agent harness** dropdown above the input and choose **Claude Code**.
 * **Oz web app** - On the new run or new schedule pane, choose **Claude Code** in the **Harness** field. A **Claude Code auth secret** field appears below it; pick one of your stored Anthropic secrets.
 * **API and SDK** - Set the agent config `harness` to `claude` and the Anthropic secret name on the matching auth-secret field. See the [API reference](/reference/api-and-sdk/).
 

src/content/docs/agent-platform/cloud-agents/harnesses/codex.mdx

@@ -35,13 +35,13 @@ Codex calls OpenAI directly using credentials your team provides. Oz supports on
 
 * **OpenAI API key** - The Codex harness authenticates to OpenAI using this key for every run.
 
-OpenAI bills your account directly for inference. Warp credits cover the rest of the platform — environment compute, triggers, observability.
+OpenAI bills your account directly for inference. Warp credits cover the rest of the platform — environment compute, triggers, and observability.
 
 For setup steps, see [Connecting Codex credentials](/agent-platform/cloud-agents/harnesses/authentication/#connecting-codex-credentials).
 
 ## Starting a Codex run
 
-* **Warp app** - In Cloud Mode, click the harness dropdown above the input and choose **Codex**.
+* **Warp app** - In Cloud Mode, click the **Agent harness** dropdown above the input and choose **Codex**.
 * **Oz web app** - On the new run or new schedule pane, choose **Codex** in the **Harness** field. A **Codex auth secret** field appears below it; pick the OpenAI secret your team has stored.
 * **API and SDK** - Set the agent config `harness` to `codex` and the OpenAI secret name on the matching auth-secret field. See the [API reference](/reference/api-and-sdk/).
 

src/content/docs/agent-platform/cloud-agents/harnesses/index.mdx

@@ -13,14 +13,14 @@ Oz can run third-party agents — [Claude Code](/agent-platform/cloud-agents/har
 
 Third-party harnesses inherit the same Oz platform features as Warp Agent:
 
-* **Triggers** — Slack, Linear, schedules, CI, and API [triggers](/agent-platform/cloud-agents/integrations/) launch any harness.
+* **Triggers** — Slack, Linear, schedules, CI, and API [triggers](/agent-platform/cloud-agents/triggers/) launch any harness.
 * **Environments and secrets** — Reuse the same [environments](/agent-platform/cloud-agents/environments/) and [agent secrets](/agent-platform/cloud-agents/secrets/).
 * **Skills and Rules** — Saved [Skills](/agent-platform/capabilities/skills/) and [Rules](/agent-platform/capabilities/rules/) apply across harnesses.
 * **Observability** — Every run produces a transcript and shareable session in the [Oz dashboard](/agent-platform/cloud-agents/managing-cloud-agents/).
 
 ## Billing
 
-Claude Code and Codex call Anthropic or OpenAI directly using credentials you supply. The provider bills your account for inference. Warp credits cover the orchestration platform — environment compute, triggers, observability — but not third-party inference.
+Claude Code and Codex each call their provider directly using credentials you supply, and the provider bills your account for inference. Warp credits cover the orchestration platform — environment compute, triggers, and observability — but not third-party inference.
 
 ## How to switch harnesses
 

src/content/docs/agent-platform/cloud-agents/harnesses/warp-agent.mdx

@@ -14,15 +14,15 @@ Warp Agent is the same agent runtime that powers Agent Mode in the Warp terminal
 ## Key features
 
 * **Multi-model auto-routing** - Routes between Anthropic, OpenAI, Google, and Fireworks-hosted models. Choose a specific model, or let Warp pick via `auto`, `auto-efficient`, `auto-genius`, or `auto-open`. See [Model choice](/agent-platform/capabilities/model-choice/) for the full catalog.
-* **Full terminal and tool access** - Runs commands, edits files, reads logs, executes tests, navigates repos, and calls MCP servers — the same toolbelt the Warp Agent uses locally.
+* **Full terminal and tool access** - Runs commands, edits files, reads logs, executes tests, navigates repos, and calls MCP servers — the same toolbelt Warp Agent uses locally.
 * **Platform-native context** - Reads [Codebase Context](/agent-platform/capabilities/codebase-context/), applies [Rules](/agent-platform/capabilities/rules/), reuses saved [Skills](/agent-platform/capabilities/skills/), and respects Memory and Warp Drive context with no extra setup.
 * **Multi-repo execution** - Clones every repo configured on the [environment](/agent-platform/cloud-agents/environments/) and works across them in a single run.
 * **Cross-harness orchestration parent** - A Warp Agent parent run can spawn Claude Code or Codex [subagents](/agent-platform/cloud-agents/overview/) and coordinate their outputs. Other harnesses cannot act as parents in a multi-harness orchestration.
 * **No extra credentials** - Warp Agent uses your existing Warp account and credits. There's no separate API key to configure.
 
 ## How it works
 
-Warp Agent with Oz is the same agent runtime as Agent Mode in the Warp terminal: it plans, calls tools, edits code, runs tests, and reports progress. The cloud platform adds the [environment](/agent-platform/cloud-agents/environments/), triggers, observability, and team governance around the run, and the transcript is inspectable in real time and replayable afterward from the [Oz dashboard](/agent-platform/cloud-agents/managing-cloud-agents/).
+Warp Agent is the same agent runtime as Agent Mode in the Warp terminal: it plans, calls tools, edits code, runs tests, and reports progress. The cloud platform adds the [environment](/agent-platform/cloud-agents/environments/), triggers, observability, and team governance around the run, and the transcript is inspectable in real time and replayable afterward from the [Oz dashboard](/agent-platform/cloud-agents/managing-cloud-agents/).
 
 Team admins can disable any harness for their workspace; whichever harnesses remain are the ones available to users on that team.
 
@@ -52,7 +52,7 @@ Subagents run in the same environment as the parent and share the same secrets,
 
 Warp Agent is the default, so there's nothing extra to configure.
 
-* **Warp app** - Start a cloud agent run from the input. The harness dropdown defaults to **Warp Agent**.
+* **Warp app** - Start a cloud agent run from the input. The **Agent harness** dropdown defaults to **Warp Agent**.
 * **Oz web app** - On a new run or new schedule pane, leave the **Harness** field set to **Warp Agent**.
 * **Oz CLI** - Run `oz agent run-cloud --prompt "..."` with no `--harness` flag, or pass `--harness oz` explicitly.
 * **API and SDK** - Omit the `harness` field on the agent config, or set it to `oz`. See the [API reference](/reference/api-and-sdk/).