fix: resolve bugs in chatd streaming system (#22720)

Split from #22693 per review feedback.

Fixes multiple bugs in coderd/chatd and sub-packages including race
conditions, transaction safety, stream buffer bounds, retry limits, and
enterprise relay improvements.

See commit message for full list.

coderd/chatd/chatloop/compaction.go

@@ -123,7 +123,8 @@ func tryCompact(
 		config.SystemSummaryPrefix + "\n\n" + summary,
 	)
 
-	err = config.Persist(ctx, CompactionResult{
+	persistCtx := context.WithoutCancel(ctx)
+	err = config.Persist(persistCtx, CompactionResult{
 		SystemSummary:    systemSummary,
 		SummaryReport:    summary,
 		ThresholdPercent: config.ThresholdPercent,