fix(ui): every full-screen overlay hosts its own toasts, above the players' controls, without re-announcing them

Deep-review round 3 of bug hunt 2026-09 (the round-2 overlay toast host, finished).

- Inside an overlay the toast stack sits above the bottom band (bottom-24, the UpNextCard rung) and
  lets clicks between cards through: at the app's own spot it covered the Plex transport row and
  PlayerModal's docked bar and took their clicks while a toast was up (measured: play/pause, ±10,
  stop, prev/next, mute all hit the toast).
- ui/Modal and the onboarding wizard mount an overlay host too, so a toast raised under any dialog
  is readable and a click on it no longer closes the dialog; the Modal's Tab trap spans the whole
  dialog, so a toast's action and dismiss are keyboard-reachable. A test now enforces the
  convention: a component that covers the viewport at z-overlay must mount <Toaster overlay />.
- PlayerModal's host moves into the stage in true fullscreen (outside the element holding the lock it
  was painted under it).
- A host that takes over shows the toasts it inherits silently (no second role=alert, its region
  aria-live=off until they are in), and each countdown bar starts as far in as its toast already is
  instead of restarting while the real dismiss timer does not.
- The overlay-host registry uses lib/store instead of a hand-rolled listener triad.

frontend/src/components/PlayerModal.dom.test.tsx

@@ -270,4 +270,23 @@ describe("PlayerModal — toasts raised while it is open", () => {
     act(() => void notify({ level: "error", message: "Couldn't remove the video." }));
     expect(screen.getByTestId("player-modal").textContent).toContain("Couldn't remove the video.");
   });
+
+  it("shows them inside the stage in true fullscreen — the element holding the lock", async () => {
+    // Anything outside the fullscreen element is painted under it. The player's host sat beside the
+    // card, so in fullscreen a lost connection was reported to nobody.
+    vi.spyOn(api, "videoDetail").mockReturnValue(new Promise(() => {}));
+    const A = vid("A", 0);
+    renderModal(
+      <PlayerModal video={A} queue={[A]} startIndex={0} onClose={() => {}} onState={() => {}} />,
+    );
+    const stage = document.querySelector(".player-stage")!;
+    Object.defineProperty(document, "fullscreenElement", { configurable: true, get: () => stage });
+    try {
+      act(() => void document.dispatchEvent(new Event("fullscreenchange")));
+      act(() => void notify({ level: "error", message: "Connection lost" }));
+      await waitFor(() => expect(stage.textContent).toContain("Connection lost"));
+    } finally {
+      delete (document as { fullscreenElement?: unknown }).fullscreenElement;
+    }
+  });
 });