feat: add global chat workspace TTL setting (#23265)

- Add `agents_workspace_ttl` site config (default: whatever the template
says a.k.a. `0s`)
- Expose via GET/PUT `/api/experimental/chats/config/workspace-ttl`
- Chat tool reads setting and passes `TTLMillis` on workspace creation
- Existing autostop infrastructure handles the rest (zero changes to
LifecycleExecutor, CalculateAutostop, or activity bumping)
- ⚠️ Template-level `UserAutostopEnabled=false` overrides this global
default. Not touching this.
- Frontend: "Workspace Lifetime" control in /agents/settings Behavior
tab (admin-only)

> This PR was created with the help of Coder Agents, and has been
reviewed by several humans and robots. 🤖🤝🧑‍💻

coderd/database/queries.sql.go

@@ -16828,6 +16828,23 @@ func (q *sqlQuerier) GetChatSystemPrompt(ctx context.Context) (string, error) {
 	return chat_system_prompt, err
 }
 
+const getChatWorkspaceTTL = `-- name: GetChatWorkspaceTTL :one
+SELECT
+    COALESCE(
+        (SELECT value FROM site_configs WHERE key = 'agents_workspace_ttl'),
+        '0s'
+    )::text AS workspace_ttl
+`
+
+// Returns the global TTL for chat workspaces as a Go duration string.
+// Returns "0s" (disabled) when no value has been configured.
+func (q *sqlQuerier) GetChatWorkspaceTTL(ctx context.Context) (string, error) {
+	row := q.db.QueryRowContext(ctx, getChatWorkspaceTTL)
+	var workspace_ttl string
+	err := row.Scan(&workspace_ttl)
+	return workspace_ttl, err
+}
+
 const getDERPMeshKey = `-- name: GetDERPMeshKey :one
 SELECT value FROM site_configs WHERE key = 'derp_mesh_key'
 `
@@ -17042,6 +17059,19 @@ func (q *sqlQuerier) UpsertChatSystemPrompt(ctx context.Context, value string) e
 	return err
 }
 
+const upsertChatWorkspaceTTL = `-- name: UpsertChatWorkspaceTTL :exec
+INSERT INTO site_configs (key, value)
+VALUES ('agents_workspace_ttl', $1::text)
+ON CONFLICT (key) DO UPDATE
+SET value = $1::text
+WHERE site_configs.key = 'agents_workspace_ttl'
+`
+
+func (q *sqlQuerier) UpsertChatWorkspaceTTL(ctx context.Context, workspaceTtl string) error {
+	_, err := q.db.ExecContext(ctx, upsertChatWorkspaceTTL, workspaceTtl)
+	return err
+}
+
 const upsertDefaultProxy = `-- name: UpsertDefaultProxy :exec
 INSERT INTO site_configs (key, value)
 VALUES