chore(code): rename claude -> claude code, format glm name (#3055)

## Problem

1. "claude" in the model switcher might not be super clear that it's claude code harness
2. glm model name is wonky

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## Changes

1. rename "switch to claude" -> "switch to claude code"
2. format cf model names

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## How did you test this?

manually

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## Automatic notifications

- [ ] Publish to changelog?
- [ ] Alert Sales and Marketing teams?

Author: adboio

packages/agent/src/gateway-models.test.ts

@@ -55,6 +55,18 @@ describe("formatGatewayModelName", () => {
     ).toBe("gpt-5.5");
   });
 
+  it("formats Cloudflare models as the lowercase final path segment", () => {
+    expect(
+      formatGatewayModelName({
+        id: "@cf/zai-org/glm-5.2",
+        owned_by: "cloudflare",
+        context_window: 128000,
+        supports_streaming: true,
+        supports_vision: false,
+      }),
+    ).toBe("glm-5.2");
+  });
+
   it("blocks deprecated Claude gateway models", () => {
     expect(isBlockedModelId("claude-opus-4-5")).toBe(true);
     expect(isBlockedModelId("claude-opus-4-6")).toBe(true);

packages/agent/src/gateway-models.ts

@@ -221,6 +221,10 @@ export function getClaudeModelRecency(modelId: string): number {
 const PROVIDER_PREFIXES = ["anthropic/", "openai/", "google-vertex/"];
 
 export function formatGatewayModelName(model: GatewayModel): string {
+  if (isCloudflareModel(model)) {
+    return (model.id.split("/").pop() ?? model.id).toLowerCase();
+  }
+
   if (isOpenAIModel(model)) {
     return stripProviderPrefix(model.id).toLowerCase();
   }

packages/ui/src/features/sessions/components/UnifiedModelSelector.tsx

@@ -31,7 +31,7 @@ const ADAPTER_ICONS: Record<AgentAdapter, React.ReactNode> = {
 };
 
 const ADAPTER_LABELS: Record<AgentAdapter, string> = {
-  claude: "Claude",
+  claude: "Claude Code",
   codex: "Codex",
 };