[XY-code1]

Summary

Fixes #386.

Make session idle expiration observable without changing the default five-minute
timeout or daemon-global --session-idle configuration.

Changes

• Add optional last_activity_at_ms, idle_timeout_ms, and idle_protected
  fields to session-list entries.
• Show the estimated remaining idle lifetime in human-readable
  bsk session list output, or paused while active browser cooperation
  protects the session from idle reaping.
• Preserve a structured session_idle_timeout reason after the idle reaper
  successfully stops a session.
• Bound the process-local stop-reason cache to 1,024 entries with a 10-minute
  TTL, cleaning expired entries on reads and writes.
• Keep lifecycle metadata out of system.status.
• Document the timeout behavior and lifecycle output.

The cache stores only session IDs and monotonic timestamps. It is not persisted
and contains no URL, title, form, or page data.

Compatibility

• The default timeout remains five minutes.
• --session-idle remains daemon-global.
• BrowserSkill tool activity refreshes the deadline.
• The current main cooperation lifecycle is preserved: active cooperation
  pauses idle reaping, and ending it starts a fresh idle interval.
• No keepalive command is introduced.
• New protocol fields are optional, so newer clients accept older daemon
  responses and older clients can ignore the additional fields.

Validation

Passed locally on the merged head:

• cargo fmt --check
• cargo test -p bsk --test cli_parse --locked — 44 passed
• cargo test -p bsk-protocol --locked — 172 passed
• cargo test -p bsk daemon::sessions --locked — 9 passed
• browser_skill_tool_activity_renews_the_idle_deadline — passed
• git diff --check
• git diff --cached --check

Two focused sessions_ipc cases still cannot complete on this Windows host
because the test client cannot connect to the temporary named-pipe endpoint:

• session_idle_timeout_stops_unregisters_and_explains_later_use
• session_list_reports_non_sensitive_idle_lifecycle_metadata

Hosted CI must verify those cases. pnpm lint is also not complete locally
because this Windows checkout presents repository-wide CRLF formatting
differences, and pnpm ext:test stops before executing tests because Vite/OXC
cannot resolve the existing apps/extension/tsconfig.json. No unrelated files
were changed to mask either environment failure.

[XY-code1]

@iuyo5678 Could you please review this PR and approve the hosted workflow when convenient?

I have merged the latest main and resolved the session-lifecycle conflict by preserving the new cooperation idle protection while keeping this PR's observability and bounded timeout-reason retention. bsk session list now reports paused during protected cooperation instead of showing a misleading countdown, and the optional JSON projection exposes that state without page-sensitive data.

The focused Rust checks pass on the merged head (44 CLI parsing tests, 172 protocol tests, and 9 session-registry tests). One new activity-renewal IPC test also passes locally; the two named-pipe lifecycle cases remain explicitly listed in the PR description for Hosted CI verification.

I would especially appreciate review of the optional protocol fields, cooperation/idle interaction, and the 10-minute/1,024-entry process-local stop-reason bound. Thank you!