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/database/queries/siteconfig.sql

@@ -302,3 +302,17 @@ INSERT INTO site_configs (key, value)
 VALUES ('agents_chat_retention_days', CAST(@retention_days AS integer)::text)
 ON CONFLICT (key) DO UPDATE SET value = CAST(@retention_days AS integer)::text
 WHERE site_configs.key = 'agents_chat_retention_days';
+
+-- name: GetChatAutoArchiveDays :one
+-- Auto-archive window in days. 0 disables.
+SELECT COALESCE(
+    (SELECT value::integer FROM site_configs
+     WHERE key = 'agents_chat_auto_archive_days'),
+    @default_auto_archive_days::integer
+) :: integer AS auto_archive_days;
+
+-- name: UpsertChatAutoArchiveDays :exec
+INSERT INTO site_configs (key, value)
+VALUES ('agents_chat_auto_archive_days', CAST(@auto_archive_days AS integer)::text)
+ON CONFLICT (key) DO UPDATE SET value = CAST(@auto_archive_days AS integer)::text
+WHERE site_configs.key = 'agents_chat_auto_archive_days';