serve: live board via SSE (subscribe + re-render)

[andreiRS]

Part of the serve-board spec (docs/specs/serve-board.md), architecture in docs/adr/0016-board-server-reuses-core-in-process.md.

Effort

M — client SSE subscription + re-render.

What to build

Subscribe the board to GET /api/events and re-render lanes/cards when a new snapshot arrives, so the board updates live as agents or other viewers change the Store — no manual refresh. Reconcile with any in-flight optimistic state per the S9 model.

Acceptance criteria

• An out-of-band tasks mv (or another viewer's action) updates the open board within a moment, no refresh.
• Live updates do not clobber an in-flight optimistic local change incorrectly.
• Reconnects gracefully if the stream drops.

Blocked by

#18, #17

[andreiRS]

Done on feat/serve-board. The board subscribes to GET /api/events and re-renders wholesale on every snapshot, reconciling in-flight optimistic state per the write-interaction spec §3/§5.

Commits:

• 383e748 green: live board via SSE — subscribe + wholesale reconcile
• 094cca4 refactor(slice): address review — post-dates check by sha, not same-second timestamp
• 4d691fb refactor(slice): address review — self-healing SSE reconnect + reconnecting hint

Also folded in the deferred #19 items: removed the per-move /api/board refetch (SSE now reconciles), added the stale-snapshot ordering guard (by head.committed_at) and the post-dates-the-write reconcile check (by head.sha, so a move committing in the same wall-clock second as its issued head still clears its pending overlay).

Verified end-to-end in a real browser against the single-origin production server (built web/dist served by tasks serve, no dev proxy):

• AC1: an out-of-band tasks mv updates the open board within ~1s, no refresh.
• AC2: a drag reconciles via the commit's SSE frame (no refetch) with no stuck pending overlay; optimistic state is not clobbered.
• AC3: killing the server keeps the last board visible with a subtle 'reconnecting…' hint (not the hard error screen); on restart the self-healing reconnect loop re-establishes the stream, catches the board up to changes made while it was down, and resumes live updates.

Note for reviewers: the Vite dev proxy (bun run dev) does not reliably stream SSE concurrently with a POST, so live updates appear to stall after a write in dev only. The compiled-binary / single-origin path is unaffected. Worth a proxy-config follow-up or a dev-README note.

Gates green: root + web tsc --noEmit, clean bun run build.