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.

> 🤖

coderd/audit/fields.go

@@ -10,7 +10,8 @@ import (
 type BackgroundSubsystem string
 
 const (
-	BackgroundSubsystemDormancy BackgroundSubsystem = "dormancy"
+	BackgroundSubsystemDormancy        BackgroundSubsystem = "dormancy"
+	BackgroundSubsystemChatAutoArchive BackgroundSubsystem = "chat_auto_archive"
 )
 
 func BackgroundTaskFields(subsystem BackgroundSubsystem) map[string]string {