email: move the mail store and every route into the sidecar

Email was the one sidecar built inside out. The platform held ~1,800 lines — the per-account
SQLite store, all 14 HTTP routes, account CRUD, resync, IMAP validation — while the 314-line
sidecar was a scheduler that reached BACK into the platform to do anything
(`import { performResync } from '../../api/email/resync'`).

The sidecar now serves its own HTTP listener and announces `email:server`, and
/api/email/* on the platform is createSidecarProxy like every other one: 1,801 lines down
to 22, with no mail knowledge left in it — not a message, not a folder, not a credential.

The routes moved verbatim, Hono and all. http.ts only reconstructs what the platform's
middleware used to provide: `user` on the context, from the X-Officer-User header the proxy
injects (trusted because this server binds loopback), and an error handler that turns
custom-errors into status codes.

The /email/events SSE stream went with them, which removes a whole round trip: the IDLE
watcher used to send `email:new` over the registration socket so the platform could push to
its SSE clients. Those clients are here now, so it calls broadcastEmailNew in-process and
`email:new` is gone from the wire protocol.

DELIBERATELY NOT DONE YET, and left backwards on purpose rather than half-moved:

- The two sync handlers (email-sync 381 lines, gmail-sync 712) still run in the platform's
  queue and now import the store from its new home — a platform → sidecar import, which is
  the wrong direction and is temporary. Moving them is option (A) from the plan: the sidecar
  schedules its own syncs, independent of the platform Jobs list.
- accounts.ts still imports queue/init to enqueue a sync and to report sync status, and
  index.ts still carries the queue-over-WS shim that inversion needs.
- The three channel handlers still open the mail store directly rather than asking over HTTP.

Two things worth knowing while testing: a from-scratch sync holds a proxied request open
well past the 60s idle default, hence timeoutSeconds on the proxy; and `gmail-sync` is
hardcoded in all three channel handlers even though the only account is provider=gmail with
auth_type=password, which routes to IMAP — so "sync emails" from a chat channel is
almost certainly already broken, and folds into the next stage.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/servers/sidecar/protocol.ts

@@ -50,8 +50,7 @@ export type SidecarEvent =
   | { type: 'vnc:stopped'; id: string }
   | { type: 'vnc:status'; id: string; session: VncSessionInfo | null }
   | { type: 'vnc:error'; id: string; error: string }
-  // Email
-  | { type: 'email:new'; userEmail: string }
+  // Email — new mail no longer crosses this socket; the sidecar owns the SSE stream and pushes directly
   // OpenCode — the sidecar reports where its `opencode serve` is listening (random port) on connect
   | { type: 'opencode:server'; port: number }
   // OpenCode turn streaming (analog of claude:*): spawned ack, per-message stream, session id report
@@ -78,6 +77,8 @@ export type SidecarEvent =
   | { type: 'wallet:server'; port: number }
   // PTY — the sidecar reports where its terminal HTTP/WS server is listening (random port) on connect
   | { type: 'pty:server'; port: number }
+  // Email — the sidecar reports where its mail HTTP server is listening (random port) on connect
+  | { type: 'email:server'; port: number }
   // Generic
   | { type: 'error'; id?: string; error: string };