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/batch.go

@@ -51,7 +51,9 @@ func (r batchResult) PublicJSON() ([]byte, error) { return json.Marshal(r) }
 // instead. Each round's grounded Side quests are stored before the next
 // round starts, so the deck fills as the batch goes. The batch ends done
 // or failed; Side quests stored before a failure stay in the deck. When
-// recording the batch's end fails, so does the job.
+// recording the batch's end fails, so does the job; when it times out at
+// shutdown, the job is left running and the batch with it, for the next
+// start to fail.
 func (s *Service) runBatch(ctx context.Context, p BatchJob, publish func(batchResult) error) (batchResult, error) {
 	n, err := db.New(s.st.Writer).StartSuggestionBatch(ctx, db.StartSuggestionBatchParams{
 		UpdatedAt: store.Now().String(),
@@ -64,14 +66,13 @@ func (s *Service) runBatch(ctx context.Context, p BatchJob, publish func(batchRe
 		return batchResult{}, fmt.Errorf("suggest: batch %s is not pending", p.BatchID)
 	}
 	res, err := s.fill(ctx, p.BatchID, publish)
-	write := context.WithoutCancel(ctx)
 	if err == nil {
-		if err := s.finishBatch(write, p.BatchID, BatchDone); err != nil {
+		if err := s.finishBatch(ctx, p.BatchID, BatchDone); err != nil {
 			return batchResult{}, err
 		}
 		return res, nil
 	}
-	finishErr := s.finishBatch(write, p.BatchID, BatchFailed)
+	finishErr := s.finishBatch(ctx, p.BatchID, BatchFailed)
 	if ctx.Err() != nil {
 		return batchResult{}, errors.Join(ctx.Err(), finishErr)
 	}