feat: auto-archive inactive chats with audit trail (#24642)

Adds a background job in `dbpurge` that periodically archives chats
inactive beyond a configurable threshold. Each archived root chat gets a
background audit entry tagged `chat_auto_archive`. Disabled by default.

* New `AutoArchiveInactiveChats` SQL query with LATERAL last-activity
subquery and partial index on archive candidates
* `site_configs`-backed `auto_archive_days` setting with admin-only PUT,
any-authenticated-user GET
* Cascade archive via `root_chat_id`; pinned chats and active threads
exempt
* Root-only audit dispatch on detached context, matching manual archive
(`patchChat`) behavior
* 11 subtests covering disabled no-op, boundary, deleted messages, child
activity, pinned exemption, multi-owner, idempotency, and batch
pagination

PR #24643 adds per-owner digest notifications.
PR #24704 adds the requisite UI controls.

> 🤖

cli/server.go

@@ -1074,7 +1074,7 @@ func (r *RootCmd) Server(newAPI func(context.Context, *coderd.Options) (*coderd.
 			defer shutdownConns()
 
 			// Ensures that old database entries are cleaned up over time!
-			purger := dbpurge.New(ctx, logger.Named("dbpurge"), options.Database, options.DeploymentValues, quartz.NewReal(), options.PrometheusRegistry)
+			purger := dbpurge.New(ctx, logger.Named("dbpurge"), options.Database, options.DeploymentValues, options.PrometheusRegistry, &coderAPI.Auditor)
 			defer purger.Close()
 
 			// Updates workspace usage