[Fix] Slack working indicator disappears when an earlier turn receives its title

[roomote-roomote]

​Opened on behalf of @daniel-lxs. View the task or mention @roomote-roomote for follow-up asks.

Related issue

No issue opened. This is a scoped internal reliability fix.

Why this PR exists

• A maintainer explicitly invited this PR in the linked issue or discussion
• I am a maintainer / this is internal Roomote work

A completed short Fast turn could receive its generated title after the next turn started. That callback set the shared Slack session to active, clearing the newer turn's working indicator.

What changed

Initialize the idle Slack session during short-turn settlement, even when its title is not ready. Later title callbacks only rename the session and never write its status. This preserves delayed titles without a process-local ownership registry.

Extend the existing mock Slack server to retain agent session status and title so the actual notifier/WebClient HTTP path can be checked through /mock/state.

Impact: late titles no longer clear newer processing status. Untitled short turns now incur one extra Slack request during settlement; the 300 ms processing delay remains unchanged. Broader lock-loss cleanup and retry-indicator behavior are not changed.

How it was tested

Classification: draft awaiting proof. Focused automated and HTTP-adapter evidence passes; live end-to-end Slack orchestration/rendering remains unverified.

• Before the fix, the new titled and untitled two-turn regressions both reproduced the stale active status write.
• 141 tests passed across fast-agent-session-activity.test.ts, fast-agent-session-activity.integration.test.ts, agent-session-title-sync.test.ts, mock-slack-server.test.ts, and slack-notifier.test.ts using pnpm exec dotenvx run -f .env.test -- pnpm --filter @roomote/slack exec vitest run with those paths.
• pnpm --filter @roomote/slack check-types, changed-file oxfmt, and git diff --check passed.
• Pre-push oxlint, residual ESLint, repository fast typechecks, and knip passed; knip emitted a non-failing existing configuration hint for the docs mint binary.
• The HTTP integration test drives the real activity adapter, SlackNotifier, and WebClient against the checked-in mock server. It verifies active -> processing -> late rename while still processing -> active on the newer turn's settlement. Title locking is substituted with notifier rename; Redis title synchronization has separate tests. No inbound webhook or inference turn is replayed, and no live Slack workspace is contacted.
• Browser capture is not applicable to this backend lifecycle claim. No screenshots are presented as evidence.

Before promoting readiness, replay two successive Fast turns through the full inbound Slack path with a delayed first title and verify native working status plus title persistence. This is not a claim that Slack indicators cover background coding or retry waits.

Checklist

• The PR title follows the repo convention: [Fix], [Feat], [Improve], [Refactor], [Docs], or [Chore] followed by a user-facing description
• This PR is small and scoped to one change
• pnpm lint and pnpm check-types pass locally
• I added tests or included a clear manual validation note above
• I removed secrets, tokens, private keys, and customer data from code, logs, and screenshots
• If this change should appear in the changelog, I ran pnpm changeset

The full formatting-inclusive lint and tsc monorepo commands were not run; the pre-push fast gates and package tsc passed. No changeset was added.

[roomote-community]

No code issues found. See task

_{Reviewed 9549211}