feat(sessions): add compact option to stale conversation cost warning

[charlesvien]

Problem

When a large, idle conversation's prompt cache has expired, staff get a warning that continuing will re-process the whole thread at full input price (the "≈$33" notice). The dialog only offered two ways out: Continue anyway (pay the full reload) or Not now (pause). There was no way to keep the thread's context without the expensive reload, so the useful middle option — compacting — was missing.

Changes

Add a Compact instead action to StaleConversationCostDialog. It runs the agent's existing manual-compaction command (/compact), summarizing the history so the thread's context shrinks to a fraction of its size instead of being reloaded whole or thrown away.

• StaleConversationCostDialog gains an onCompact prop and a third button; the copy now names compaction as the cheap middle path.
• SessionView wires onCompact to acknowledge the gate (closing the dialog and unlocking the composer) and send /compact, which surfaces the usual "Compacting conversation history…" progress.

Screenshots: n/a (copy + one button in an existing dialog).

How did you test this?

• biome check on both changed files (clean).
• Manual reasoning through the gate flow: /compact is the same command the context-error tip already directs users to type, sent through the normal prompt path, so it queues/spawns like any message and drives the existing compaction UI.

Automatic notifications

• Publish to changelog?
• Alert Sales and Marketing teams?

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Created with PostHog from a Slack thread

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[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit a8bf734.}

[greptile-apps]

_{Reviews (1): Last reviewed commit: "feat(sessions): add compact option to st..." | Re-trigger Greptile}

[github-actions]

Small UI-only change that adds a "Compact instead" button to the stale session cost dialog. The implementation is straightforward — it reuses the existing onContinue gate-clear path and dispatches /compact via onSendPrompt. No data models, API contracts, or business logic touched.