feat(ui): finish the workspace-sessions plan — tool filter, session search, explicit Resume

- Sidebar: a tool filter (shown once workspaces of two tools exist, kept in
  agenthub.sidebar.projects → tool; reordering under it keeps the hidden
  workspaces' places), and search that also finds a workspace by one of its
  session names, showing only the matching sessions.
- Workspace home: the repository it belongs to (root, main branch, worktree
  count) under the title, and each recent's cost.
- Transcript page: an explicit Resume for a Claude session started in a
  workspace's own folder (SessionResumeButton). It warns that a resume re-reads
  the whole transcript, re-reads the live panes, then starts in the first free
  pane and opens it; a live session offers Open pane instead.

client/src/components/lanes/__tests__/WorkspaceHome.test.tsx

@@ -36,7 +36,7 @@ vi.mock("../../run/RunSetup", () => ({
 let view: LaneSourcesView;
 let runs: RunHandle[];
 const sessions = [
-  { id: "s-live", name: "Live one", started_at: "2026-09-30T10:00:00Z" },
+  { id: "s-live", name: "Live one", started_at: "2026-09-30T10:00:00Z", cost: 1.234 },
   { id: "s-old", name: "Old one", started_at: "2026-09-29T10:00:00Z" },
 ] as Session[];
 
@@ -208,6 +208,36 @@ describe("WorkspaceHome", () => {
     expect(api.lanes.action).not.toHaveBeenCalled();
   });
 
+  it("names the repository it belongs to: root, main branch, worktree count", async () => {
+    renderHome();
+    const facts = await screen.findByTestId("workspace-home-facts");
+    expect(facts).toHaveTextContent("/r");
+    expect(facts).toHaveTextContent("main");
+    expect(facts).toHaveTextContent("3 worktrees");
+  });
+
+  it("shows no repository line for a workspace outside any repository", async () => {
+    vi.mocked(api.projects.list).mockResolvedValueOnce({
+      projects: [{ root: null, name: "plain", workspaces: [1], worktrees: [] }],
+    } as never);
+    renderHome();
+    await waitFor(() => expect(api.projects.list).toHaveBeenCalled());
+    expect(screen.queryByTestId("workspace-home-facts")).toBeNull();
+  });
+
+  it("shows no repository line for a folder in no git project", async () => {
+    renderHome(lane({ id: 9, cwd: "/plain" }));
+    await waitFor(() => expect(api.projects.list).toHaveBeenCalled());
+    expect(screen.queryByTestId("workspace-home-facts")).toBeNull();
+  });
+
+  it("shows a recent's cost when it has one", async () => {
+    renderHome();
+    const live = await screen.findByTestId("workspace-recent-s-live");
+    expect(live).toHaveTextContent("$1.23");
+    expect(screen.getByTestId("workspace-recent-s-old")).not.toHaveTextContent("$");
+  });
+
   it("saves instructions", async () => {
     const user = userEvent.setup();
     renderHome();