feat(agent): implement /clear command

[haacked]

Problem

Typing /clear in PostHog Code reports "Unsupported slash command". Upstream hid the SDK's own /clear because it is unreliable in this embedding, but users still want a way to drop the conversation and free up context without abandoning the task, including on cloud runs, where the append-only session log is what rehydrates the conversation on resume.

Here's an example session that shows it works.

Refs #670

Changes

• Claude adapter (packages/agent): prompt() intercepts /clear (never forwarded to the SDK). It retires the current SDK query (reusing the refreshSession teardown, now extracted as retireQuery) and swaps in a brand-new SDK session, fresh id, no resume, under the same ACP session. The ACP session id stays stable; the new Session.sdkSessionId tracks the underlying SDK session, and hasSession accepts either id so cancel/reconnect work from both sides. /clear is advertised in the command list again.
• Session log / cloud resume: the clear is recorded as a _posthog/conversation_cleared marker plus an updated sdk_session mapping in the append-only log. rebuildConversation (jsonl hydration + ResumeSaga) treats the marker as a boundary, and ResumeSaga.findSessionId picks up the post-clear session id, so cloud sandbox restarts and desktop cold reconnects resume the fresh SDK session with only post-clear turns.
• UI: the transcript keeps the full history and renders a "Conversation cleared" divider (like the compaction marker); the context indicator resets to zero via a usage_update.
• Timeout and reconnect hardening: the /clear prompt is only broadcast (and thus logged) once the new session is confirmed live, so a timeout leaves no orphaned entry in the log. A "Clearing…" status indicator mirrors the existing compaction spinner, so a slow or failed clear gives the user feedback instead of going silent, with a clearing_failed row rendering the outcome. On success, the local session file left under the original session id gets deleted so a cold reconnect can't mistake it for current and resume the pre-clear conversation. /clear also now refuses while a turn is queued, not just while one is active.

Codex sessions are unchanged, /clear is Claude-adapter only for now.

How did you test this?

• New unit tests: adapter /clear behavior (fresh session swap, marker/mapping emission, busy/queued-turn guards, refresh-after-clear, timeout handling, stale jsonl cleanup, resumeSession id matching after a clear), command advertisement, clear-boundary handling in jsonl hydration and ResumeSaga, and the UI divider and status-row rendering (including clearing/clearing_failed).
• Ran the full @posthog/agent suite, @posthog/ui sessions suite, and pnpm typecheck for agent/core/ui plus Biome on the touched packages.

Automatic notifications

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

Why: /clear is a frequently reached-for command that PostHog Code currently rejects; implementing it cloud-first required making the session-log rehydration clear-aware.

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Created with PostHog Code

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[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit e0d3e15.}