fix(updates): report a plugin build installed beside the running one, never "up to date" on a failed check

A `claude plugin update` run from a terminal (or with only the Claude desktop
app open) unpacks the new build and starts nothing: no SessionStart fires, so
the dashboard kept running the old cache dir across reboots, and with the
forge unreachable the sidebar read "Up to date" (seen on a machine stuck at
1.8.10).

- pluginStatus asks supersededBy for its own root: a recorded sibling install
  sets `installed_not_running: {root, version}` and `update_available`, with
  no network needed
- the sidebar reads "<version> installed, not running"; the update modal keys
  on it, so Update now is offered even with no release tag or sha
- plugin-update-helper hands over to the recorded install first, the newest
  sibling dir only as a fallback
- a plugin install whose release lookup failed reads "Could not check for
  updates" instead of "Up to date"
- docs/PLUGINS.md: the case and the manual hand-over command

client/src/components/__tests__/Sidebar.test.tsx

@@ -5,10 +5,11 @@
  */
 
 import { describe, it, expect } from "vitest";
-import { render, screen, waitFor } from "@testing-library/react";
+import { act, render, screen, waitFor } from "@testing-library/react";
 import userEvent from "@testing-library/user-event";
 import { MemoryRouter } from "react-router-dom";
 import { Sidebar } from "../Sidebar";
+import { eventBus } from "../../lib/eventBus";
 
 function renderSidebar(wsConnected: boolean, collapsed = false) {
   return render(
@@ -103,4 +104,44 @@ describe("Sidebar", () => {
       expect(screen.getByText("VI")).toBeInTheDocument();
     });
   });
+
+  describe("update status line", () => {
+    const plugin = {
+      git_repo: false,
+      install_kind: "plugin",
+      situation: "plugin_managed",
+      local_version: "1.8.10",
+    };
+    const publish = (data: object) =>
+      act(() => eventBus.publish({ type: "update_status", data } as never));
+
+    it("does not claim up to date when a plugin install could not read the release", () => {
+      renderSidebar(true);
+      publish({ ...plugin, update_available: false, release_check: "unreachable" });
+      expect(screen.queryByText("Up to date")).toBeNull();
+      expect(screen.getByText("Could not check for updates")).toBeInTheDocument();
+    });
+
+    it("names a build installed beside the running one", () => {
+      renderSidebar(true);
+      publish({
+        ...plugin,
+        update_available: true,
+        release_check: "unreachable",
+        installed_not_running: { root: "/x", version: "1.8.12" },
+      });
+      expect(screen.getByText("1.8.12 installed, not running")).toBeInTheDocument();
+    });
+
+    it("still says up to date when the release was read and matches", () => {
+      renderSidebar(true);
+      publish({
+        ...plugin,
+        update_available: false,
+        release_check: "ok",
+        latest_release: "v1.8.10",
+      });
+      expect(screen.getByText("Up to date")).toBeInTheDocument();
+    });
+  });
 });