PR monitor chips never retire — survive PR close and merge, session archive, and app restart; no way to clear them

Claude Desktop's GitHub-integration PR monitors don't auto-archive when their PR closes — or even when it merges (a MERGED PR with green checks still shows a live monitor chip). The chips also survive archiving the session that created them and full app restarts, and there's no programmatic surface (MCP tool / CLI) to clear them. Meanwhile the monitor's "Auto-fix CI & address comments" automation stays armed against PRs whose head branches have been deleted (chip shows "No checks reported yet").

Repro:

1. Open several PRs from a session (gh CLI).
2. Land them locally (rebase + ff-merge + push) — GitHub marks some Closed rather than Merged depending on ref-push order; merge one normally so it's MERGED.
3. Delete the head branches; archive the originating session; restart the app.
4. All monitor chips persist indefinitely — Closed, Merged, green or gray alike.

Requests:

1. Auto-archive monitors on PR close and merge by default (or expose that in Auto-archive settings).
2. A per-chip "stop monitoring / archive now" action.
3. Disarm "Auto-fix CI" when the PR is closed or its head branch is deleted.

Environment: macOS 26.5 (arm64), Claude Desktop 1.9659.2 with bundled Claude Code; GitHub integration connected.

Related (PR-monitoring family, not duplicates): #62928 (monitoring no-ops on some CI setups), #63222 (status-polling rate limits), #64460 (wake-message config) — this issue covers monitor lifecycle/retirement, which none of those address.