feat(questions): add questions page with open count badge

Add /questions page and a nav badge with the open count.
Core decides which question is open. The page only shows and answers.
Move RatingStars out of BacklogCard so both pages share it.

README.md

@@ -252,6 +252,17 @@ flowchart LR
     Dialog -->|"community row, login"| Owners["Core /api/stats/owners"]
     Landing["Landing user tiles, login"] --> Users["Auth /api/stats/users"]
 ```
+- `/questions` (`QuestionsPage`, nav item with the open count; the badge is hidden on the page, whose title shows the
+  live count) lists one card per game with an open question (Start it? / Finished? / Dropped? / Rate it?). Core decides
+  which question is open; `src/utils/questions.js` only loads the list and sends the answer. A yes to Finished? gets
+  the Rate it? card back at once. `409` / `404` reload the list. `RatingStars` is shared with `BacklogCard`.
+
+```mermaid
+flowchart LR
+    Header["AppHeader badge"] --> Count["Core /api/library/questions/count"]
+    Page["QuestionsPage"] --> List["Core /api/library/questions"]
+    Page -->|"Yes / No / stars"| Answer["Core POST /api/library/questions/{appid}"]
+```
 - Owner and user lists (`src/components/people/`, `src/utils/people.js`) need a login and show listed users by name
   (a link to `/u/<name>`), everyone else as "+N private", the viewer as "You". The setting "show me in owner lists" is
   saved on its own (`PUT /api/users/settings/owner-lists`), never through `saveSettings`.