Bound the suggestion batch's end write like a job's final write

runBatch recorded the batch's end with an uncancellable context and no
deadline, before its handler returned, so a writer connection that
stayed busy could hold the worker, and shutdown, open indefinitely.

jobs.FinalWriteContext now gives every final write one bounded attempt
context (FinalWriteTimeout, 5 seconds, not cancelled with ctx); the
runner's record and finishBatch both use it. On timeout at shutdown the
handler returns, the job and batch stay running, the next Start fails
the job as interrupted and the next StartBatch fails the orphaned batch.

TestBlockedBatchEndDoesNotHoldShutdown holds the writer while a batch
reaches finishBatch and asserts the worker stops within the bound and
the batch is reconciled after restart. TestBlockedFinalWriteDoesNotHoldShutdown
no longer sets a runner field, so it compiles against earlier heads.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

internal/suggest/suggest.go

@@ -217,11 +217,16 @@ func (s *Service) startBatch(ctx context.Context, tx *sql.Tx, trigger string) (B
 	return Batch{ID: row.ID, JobID: jobID, Trigger: row.Trigger, Status: row.Status, Created: true}, nil
 }
 
-// finishBatch records running batch id as status. Its job's handler
-// returns any error, so the job never ends succeeded with the batch still
-// running; the runner keeps only a code, so the error is logged too.
+// finishBatch records running batch id as status, with
+// jobs.FinalWriteContext: the write is made even when ctx has been
+// cancelled, but a writer that stays busy cannot hold its worker past
+// jobs.FinalWriteTimeout. Its job's handler returns any error, so the job
+// never ends succeeded with the batch still running; the runner keeps only
+// a code, so the error is logged too.
 func (s *Service) finishBatch(ctx context.Context, id, status string) error {
-	n, err := db.New(s.st.Writer).FinishSuggestionBatch(ctx, db.FinishSuggestionBatchParams{
+	write, cancel := jobs.FinalWriteContext(ctx)
+	defer cancel()
+	n, err := db.New(s.st.Writer).FinishSuggestionBatch(write, db.FinishSuggestionBatchParams{
 		Status:    status,
 		UpdatedAt: store.Now().String(),
 		ID:        id,