feat(cockpit): a dot on the favicon while the inbox holds work

[jtomaszewski]

The cockpit is a background tab most of the day, and the only part of it still
on screen is the tab icon. Until now that icon said nothing: whether two PRs
were waiting or none, the paw looked the same, so the only way to find out was
to switch to the tab and look.

The bell already covers the loud half of this — it interrupts when a PR lands.
This is the quiet half: while the inbox holds anything, the favicon wears a red
dot, and the dot goes away when the last review is dealt with. No permission to
grant, no switch to find; a glance at the tab strip answers "is there anything
for me?".

What it does

• web/public/favicon-dot.svg — the badged twin of the paw: the same three
  toes and pad, stood down slightly to make room for a dot in the top-right
  rather than cut away under it (at 16px a chewed toe reads as a broken icon).
  A masked gap keeps the dot a separate shape whatever colour the tab bar
  behind it is, and the dark-mode fills follow favicon.svg's own convention.
• web/src/favicon.ts — hasInboxWork is the whole decision, and it is
  deliberately the same walkable list the ‹ › arrows walk and the bell
  announces. Three ways of saying "there is work here" that would be worth
  nothing if they disagreed about which rows count.
• web/src/api.ts — fetchReviews re-badges the tab on every read. Three
  screens poll that list on their own timers; doing it in the one function they
  all go through is the only version of "the tab matches the last queue the
  cockpit saw" that cannot go stale on whichever screen forgot.

The dot tracks the inbox only — not the open-requests tab. Those are PRs you
already settled here; GitHub still listing a request is a fact about GitHub,
not work the tab should nag you about.

Verification

• pnpm typecheck && pnpm test — 390 passing, including new unit tests for
  hasInboxWork (empty queue, awaiting, ready, all-filed, one live row among
  filed ones) and faviconHref.
• pnpm build — the new asset ships in web/dist.
• Rendered both icons at 16/32/128px in a browser: all three toes intact, dot
  legible at 16px.
• Drove the real cockpit against a running server: empty inbox → favicon.svg;
  with a live row → favicon-dot.svg; back to empty → plain again.

[Copilot]

Pull request overview

Adds a “work waiting” badge to the cockpit tab icon so users can tell (at a glance, from the tab strip) whether the inbox currently contains actionable items.

Changes:

• Introduces hasInboxWork, faviconHref, and markFavicon to compute and apply a dotted favicon when the inbox has walkable work.
• Updates fetchReviews to re-derive favicon state on every queue fetch so it stays in sync across screens.
• Adds a new favicon-dot.svg asset and documents the behavior in README.md and CLAUDE.md.

Reviewed changes

Copilot reviewed 5 out of 6 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
web/src/favicon.ts	New favicon state logic (work detection + DOM update).
web/src/favicon.test.ts	Unit tests for hasInboxWork and faviconHref.
web/src/api.ts	Re-badges favicon during fetchReviews() so the tab stays accurate.
web/public/favicon-dot.svg	New dotted favicon asset (dark-mode aware).
README.md	Documents the favicon dot behavior for users.
CLAUDE.md	Updates architecture notes to include favicon badging behavior.

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[Copilot]

Pull request overview

Copilot reviewed 5 out of 6 changed files in this pull request and generated no new comments.

[github-actions]

🎉 This PR is included in version 0.22.0 🎉

The release is available on:

• npm package (@latest dist-tag)
• GitHub release

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