Fail pull with a visible error when a backup is already in progress on the remote site

[epeicher]

Related issues

• Related to STU-2098 (the server-side half — rejecting deduped backup requests with a 409 — ships separately)

How AI was used in this PR

The investigation and implementation were done with Claude Code: it traced a customer's No backup ID found log line through the pull flow to the backup dedupe response, cross-checked the diagnosis against the site's backup history and the server-side findings, and wrote the fix plus tests. The code was reviewed by the PR author.

Proposed Changes

When a pull is requested while the remote site already has a backup queued or running, the backup service dedupes the request. Studio treated that as a successful start, then silently stopped polling — the pull sat at "in progress" forever with no error, and the only trace was a No backup ID found log line. Users hit this by restarting Studio mid-pull (losing the in-memory backup ID) and retrying while the original backup was still running server-side.

With this change the pull fails fast instead of hanging: the user gets a dialog explaining that a backup is already in progress for the site and to retry in a few minutes, and the pull enters the normal failed state so it can be retried. Both server response shapes are handled — the current 200 with backup_id: 0 and the upcoming 409 with code: backup_already_in_progress — so behavior is identical across the server rollout. The 409 is an expected transient condition and is not reported to Sentry.

As a defensive measure, the backup-status poller now also surfaces an error and marks the pull failed if it ever finds no backup ID, instead of silently abandoning the operation.

Testing Instructions

• npm test -- apps/studio/src/stores/tests/sync-operations-slice.test.ts — covers the valid-ID happy path, both "backup already in progress" response shapes, and the poller guard.
• Manual reproduction (against current production servers): connect a site and start a pull, quit Studio while "Initializing remote backup…" is shown, reopen it, and immediately pull the same site again.
  • Before: the second pull hangs at "in progress" indefinitely; the log shows No backup ID found.
  • After: an error dialog reports that a backup is already in progress and suggests retrying in a few minutes; the pull shows the failed state and can be retried. Retrying after the remote backup finishes (a few minutes; visible in the site's backup activity) succeeds.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?