Closes #151.

Restore the existing animated sidebar glyph by replacing the hardcoded idle agent state with live channel-wide run activity. Aggregate committed pi LiveDoc runs across all chats, including subagents, and publish transitions through existing listing paths without opening transcript watches or waking dormant workers. Keep busy channels out of Inactive.

Suppress stale activity for dormant, archived, and unreachable channels. Rebuild activity on worker open and hosted workspace reconnect; clear on normal shutdown. A liveness sweep broadcasts worker crashes without overwriting a replacement worker’s projection.

### Validation

- `bun types`, `bun run ci`, and `git diff --check` pass. - Real gpt-6-astra smoke checks in isolated profiles: overlapping chats, completion, stop, kill, crash, initial snapshot/reopen, and a new run after restart. Listings stayed busy until the last chat finished; crash listing cleared while persisted projection remained untouched. - Native Ace-dev build: selected and unopened background channels both show activity; stopping each independently restores its # glyph. - Hosted forwarding is typechecked/reviewed, not live-deployment tested. Its indicator is intentionally suppressed when the workspace link is unavailable.

### Built in Ace

Entirely built in Ace using lanes, subagents, shell, and native desktop tools; no external editor, terminal, browser automation, or agent. Found separate worker-watch reattachment bug #153 during native dogfooding; it is outside this PR.

Merged latest main and resolved the channel field conflict by retaining both reasoning-effort admission serialization and channel-wide activity tracking. Checked the auto-merge with the all-projects view. Full `bun types` and `bun run ci` pass. Real gpt-6-astra smoke on merged source: active effort changes rejected, overlapping chats keep aggregate busy, stopping both clears it, and idle effort changes plus normal completion still work. All smoke work used an isolated profile and was cleaned up.