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/dbmock/dbmock.go

@@ -2313,6 +2313,21 @@ func (mr *MockStoreMockRecorder) GetChats(ctx, arg any) *gomock.Call {
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChats", reflect.TypeOf((*MockStore)(nil).GetChats), ctx, arg)
 }
 
+// GetChatsByWorkspaceIDs mocks base method.
+func (m *MockStore) GetChatsByWorkspaceIDs(ctx context.Context, ids []uuid.UUID) ([]database.Chat, error) {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "GetChatsByWorkspaceIDs", ctx, ids)
+	ret0, _ := ret[0].([]database.Chat)
+	ret1, _ := ret[1].(error)
+	return ret0, ret1
+}
+
+// GetChatsByWorkspaceIDs indicates an expected call of GetChatsByWorkspaceIDs.
+func (mr *MockStoreMockRecorder) GetChatsByWorkspaceIDs(ctx, ids any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatsByWorkspaceIDs", reflect.TypeOf((*MockStore)(nil).GetChatsByWorkspaceIDs), ctx, ids)
+}
+
 // GetConnectionLogsOffset mocks base method.
 func (m *MockStore) GetConnectionLogsOffset(ctx context.Context, arg database.GetConnectionLogsOffsetParams) ([]database.GetConnectionLogsOffsetRow, error) {
 	m.ctrl.T.Helper()