feat: show agent badge on workspace list (#23453)

- Adds `GET /api/experimental/chats/by-workspace` endpoint that returns
workspace_id → latest chat_id mapping
- Modifies FE to fetch this alongside the workspace list, gated on
`agents` experiment and render an "Agent" badge similar to the existing
"Task" badge in `WorkspacesTable`
- Badge links to the "latest chat" linked to the given workspace.

Notes:
- Intentionally uses `fetchWithPostFilter` for RBAC to decouple from
workspaces API — will migrate to `workspaces_expanded` view later.
- If users have multiple chats linked to the same workspace, the badge
will link to the most recently updated one.

> 🤖 This PR was created with the help of Coder Agents, and has been
reviewed by my human. 🧑‍💻

coderd/database/dbmetrics/querymetrics.go

@@ -1256,6 +1256,14 @@ func (m queryMetricsStore) GetChats(ctx context.Context, arg database.GetChatsPa
 	return r0, r1
 }
 
+func (m queryMetricsStore) GetChatsByWorkspaceIDs(ctx context.Context, ids []uuid.UUID) ([]database.Chat, error) {
+	start := time.Now()
+	r0, r1 := m.s.GetChatsByWorkspaceIDs(ctx, ids)
+	m.queryLatencies.WithLabelValues("GetChatsByWorkspaceIDs").Observe(time.Since(start).Seconds())
+	m.queryCounts.WithLabelValues(httpmw.ExtractHTTPRoute(ctx), httpmw.ExtractHTTPMethod(ctx), "GetChatsByWorkspaceIDs").Inc()
+	return r0, r1
+}
+
 func (m queryMetricsStore) GetConnectionLogsOffset(ctx context.Context, arg database.GetConnectionLogsOffsetParams) ([]database.GetConnectionLogsOffsetRow, error) {
 	start := time.Now()
 	r0, r1 := m.s.GetConnectionLogsOffset(ctx, arg)