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/coderd.go

@@ -1201,6 +1201,8 @@ func New(options *Options) *API {
 				r.Put("/workspace-ttl", api.putChatWorkspaceTTL)
 				r.Get("/retention-days", api.getChatRetentionDays)
 				r.Put("/retention-days", api.putChatRetentionDays)
+				r.Get("/auto-archive-days", api.getChatAutoArchiveDays)
+				r.Put("/auto-archive-days", api.putChatAutoArchiveDays)
 				r.Get("/template-allowlist", api.getChatTemplateAllowlist)
 				r.Put("/template-allowlist", api.putChatTemplateAllowlist)
 			})