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/querier.go

@@ -61,6 +61,10 @@ type sqlcQuerier interface {
 	// Only unused template versions will be archived, which are any versions not
 	// referenced by the latest build of a workspace.
 	ArchiveUnusedTemplateVersions(ctx context.Context, arg ArchiveUnusedTemplateVersionsParams) ([]uuid.UUID, error)
+	// Archives inactive root chats (pinned and already-archived chats skipped),
+	// cascading to children via root_chat_id. Limits apply to roots, not total
+	// rows. Used by dbpurge.
+	AutoArchiveInactiveChats(ctx context.Context, arg AutoArchiveInactiveChatsParams) ([]AutoArchiveInactiveChatsRow, error)
 	BackoffChatDiffStatus(ctx context.Context, arg BackoffChatDiffStatusParams) error
 	BatchUpdateWorkspaceAgentMetadata(ctx context.Context, arg BatchUpdateWorkspaceAgentMetadataParams) error
 	BatchUpdateWorkspaceLastUsedAt(ctx context.Context, arg BatchUpdateWorkspaceLastUsedAtParams) error
@@ -267,6 +271,8 @@ type sqlcQuerier interface {
 	// This function returns roles for authorization purposes. Implied member roles
 	// are included.
 	GetAuthorizationUserRoles(ctx context.Context, userID uuid.UUID) (GetAuthorizationUserRolesRow, error)
+	// Auto-archive window in days. 0 disables.
+	GetChatAutoArchiveDays(ctx context.Context, defaultAutoArchiveDays int32) (int32, error)
 	GetChatByID(ctx context.Context, id uuid.UUID) (Chat, error)
 	GetChatByIDForUpdate(ctx context.Context, id uuid.UUID) (Chat, error)
 	// Per-root-chat cost breakdown for a single user within a date range.
@@ -1170,6 +1176,7 @@ type sqlcQuerier interface {
 	// cumulative values for unique counts (accurate period totals). Request counts
 	// are always deltas, accumulated in DB. Returns true if insert, false if update.
 	UpsertBoundaryUsageStats(ctx context.Context, arg UpsertBoundaryUsageStatsParams) (bool, error)
+	UpsertChatAutoArchiveDays(ctx context.Context, autoArchiveDays int32) error
 	// UpsertChatDebugLoggingAllowUsers updates the runtime admin setting that
 	// allows users to opt into chat debug logging.
 	UpsertChatDebugLoggingAllowUsers(ctx context.Context, allowUsers bool) error