feat: make database.Chat auditable (#24485)

Wire database.Chat into the audit system so chat lifecycle events
(creation, patches, etc.) produce audit log entries.

Part of CODAGT-200.

> 🤖

coderd/database/dump.sql

@@ -525,7 +525,8 @@ CREATE TYPE resource_type AS ENUM (
     'workspace_app',
     'prebuilds_settings',
     'task',
-    'ai_seat'
+    'ai_seat',
+    'chat'
 );
 
 CREATE TYPE shareable_workspace_owners AS ENUM (