feat(site/src): reintroduce chat search cache invalidation - #27892

… watch paths (#27901)

Implements Phase 2 item 5 of the chats query architecture: by-workspace
cache reconciliation. Stacked on #27892; base branch
`feat/chat-search-invalidation`.

## Problem

`chatsByWorkspace` mappings (flat `Record<workspaceId, chatId>`, IDs
only, archived chats filtered server-side) go stale on
archive/unarchive, workspace binding changes, and watch events (FINDINGS
2.3). Because the client cannot re-derive archived state from the cached
map, the only correct repair for a stale mapping is synchronous removal
plus family invalidation.

## Fix

- New `removeChatFromChatsByWorkspace(queryClient, chatId)` in
`site/src/api/queries/chats.ts`: value-match removal across the
by-workspace family, reference-preserving when nothing is removed
(mirrors the `patchChatMessages` no-op pattern).
- `archiveChat.onSuccess` and the AgentsPageLayout archive-and-delete
`onSuccess` synchronously remove the mapping; the existing
`onSettled`/explicit invalidations then reconverge.
- Watch handler: `deleted` branch removes then invalidates
(remove-before-invalidate ordering); `created` root branch invalidates;
merge path invalidates behind a new `shouldInvalidateChatsByWorkspace`
predicate (`status_change`, `action_required` only; `created`/`deleted`
have their own branches, title/summary/diff/context events do not move
`updated_at` ordering); `onOpen` reconnect invalidates for convergence.
- `useChatToolInvalidations`: workspace-binding tool completion
(`create_workspace`) also invalidates by-workspace; this is the only
reconciliation path on the embed route.

## Confirmed exclusions

- No optimistic patch in `updateChatWorkspace.onMutate`; the awaited
`onSettled` invalidation already converges.
- No cancellation guard for the by-workspace family (Phase 2 item 9
territory).
- No `createChat` change (already invalidates); no ACL or pin changes.

## Known constraints

- Cascade archives remove only the event's own chat ID from the mapping;
per-family-member `deleted` events plus family invalidation repair the
rest.
- The REST `patchChat` workspace-rebind branch publishes no watch event
server-side, so cross-session manual rebinds converge only via the
acting session's `onSettled` or a WorkspacesPage remount; not fixable
client-side.

## Testing

- `chats.test.ts`: removal scoping and reference-preservation tests;
`it.each` wiring tests (archiveChat/unarchiveChat/updateChatWorkspace
onSettled, createChat onSuccess invalidate by-workspace);
synchronous-removal assertion for `archiveChat.onSuccess`; negative
assertions for `updateChatTitle` and `createChatMessage`.
- `AgentsPageLayout.test.ts`: exhaustive `ChatWatchEventKind` table for
`shouldInvalidateChatsByWorkspace`.
- `useChatToolInvalidations.test.tsx`: create_workspace regression test
extended with a seeded by-workspace bystander.

PR generated by Coder Agents.