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.

> 🤖

codersdk/chats.go

@@ -796,6 +796,11 @@ type ChatDebugStep struct {
 // Zero means disabled — the template's own autostop setting applies.
 const DefaultChatWorkspaceTTL = 0
 
+// DefaultChatAutoArchiveDays is the default auto-archive window, in
+// days, applied when no site config row exists. Zero disables
+// auto-archival.
+const DefaultChatAutoArchiveDays int32 = 0
+
 // ChatWorkspaceTTLResponse is the response for getting the chat
 // workspace TTL setting.
 type ChatWorkspaceTTLResponse struct {
@@ -823,6 +828,17 @@ type UpdateChatRetentionDaysRequest struct {
 	RetentionDays int32 `json:"retention_days"`
 }
 
+// ChatAutoArchiveDaysResponse contains the current chat auto-archive setting.
+type ChatAutoArchiveDaysResponse struct {
+	AutoArchiveDays int32 `json:"auto_archive_days"`
+}
+
+// UpdateChatAutoArchiveDaysRequest is a request to update the chat
+// auto-archive period.
+type UpdateChatAutoArchiveDaysRequest struct {
+	AutoArchiveDays int32 `json:"auto_archive_days"`
+}
+
 // ParseChatWorkspaceTTL parses a stored TTL string, returning the
 // default when the value is empty.
 func ParseChatWorkspaceTTL(s string) (time.Duration, error) {
@@ -2183,6 +2199,33 @@ func (c *ExperimentalClient) UpdateChatRetentionDays(ctx context.Context, req Up
 	return nil
 }
 
+// GetChatAutoArchiveDays returns the configured chat auto-archive period.
+func (c *ExperimentalClient) GetChatAutoArchiveDays(ctx context.Context) (ChatAutoArchiveDaysResponse, error) {
+	res, err := c.Request(ctx, http.MethodGet, "/api/experimental/chats/config/auto-archive-days", nil)
+	if err != nil {
+		return ChatAutoArchiveDaysResponse{}, err
+	}
+	defer res.Body.Close()
+	if res.StatusCode != http.StatusOK {
+		return ChatAutoArchiveDaysResponse{}, ReadBodyAsError(res)
+	}
+	var resp ChatAutoArchiveDaysResponse
+	return resp, json.NewDecoder(res.Body).Decode(&resp)
+}
+
+// UpdateChatAutoArchiveDays updates the chat auto-archive period.
+func (c *ExperimentalClient) UpdateChatAutoArchiveDays(ctx context.Context, req UpdateChatAutoArchiveDaysRequest) error {
+	res, err := c.Request(ctx, http.MethodPut, "/api/experimental/chats/config/auto-archive-days", req)
+	if err != nil {
+		return err
+	}
+	defer res.Body.Close()
+	if res.StatusCode != http.StatusNoContent {
+		return ReadBodyAsError(res)
+	}
+	return nil
+}
+
 // GetChatTemplateAllowlist returns the deployment-wide chat template allowlist.
 func (c *ExperimentalClient) GetChatTemplateAllowlist(ctx context.Context) (ChatTemplateAllowlist, error) {
 	res, err := c.Request(ctx, http.MethodGet, "/api/experimental/chats/config/template-allowlist", nil)