feat(library): finish games from the ending achievement or suggest it

readme.md

@@ -31,6 +31,14 @@ To Be Played is split into three repositories:
   games closest to 100 %.
 - **Playtime history**: one row per game and day, for the activity view and the "most played in the last two weeks"
   dashboard banner.
+- **Finished from achievements or playtime**: `EndingAchievement` finds the one achievement of a game that means
+  "story end" (English text rule, Steam's global unlock rate between 1 and 80 %, the easiest variant wins, more than
+  3 candidates = a game without one end). When the user unlocks it, never chose the status and never answered
+  "Not yet", the achievement sync sets FINISHED, but only for a certain ending: its text says so and no other
+  achievement of the game could be the end. A status the user chose is never changed; such games get a hint on the game page instead. A second,
+  weaker hint compares the playtime with IGDB's normal time to beat (at least 90 %), only for games IGDB does not
+  mark as endless (sandbox, survival, 4X, simulator, MMO). "Not yet" hides a hint per game; a dismissed playtime hint
+  still lets the ending hint through.
 - **Hide games**: a user can hide a Steam game (e.g. a playtest or a tool). It leaves every list and number: library,
   picker, Pile of Shame, activity, achievement summary, public profile and landing page stats. The sync still
   updates its playtime, but no achievements, time to beat, moods or speedrun data are fetched for it. The library
@@ -65,6 +73,7 @@ accepted only by `GET /api/public/profiles/library` in the `X-Profile-Ticket` he
 | `GET` | `/api/library/games`, `/api/library/games/{appid}` | JWT |
 | `PUT` | `/api/library/games/{appid}/backlog` | JWT |
 | `PUT` | `/api/library/games/{appid}/status` (status only, keeps rating, notes, priority) | JWT |
+| `PUT` | `/api/library/games/{appid}/finished-hint` (`{dismissed: ENDING\|PLAYTIME}`, "Not yet"; `204`) | JWT |
 | `PUT` | `/api/library/games/{appid}/hidden` (`{hidden}`; `409 MANUAL_GAME` for a game added by hand) | JWT |
 | `POST` | `/api/library/sync` | JWT |
 | `POST` | `/api/library/broken-images` (`{appid, kind}`, kind `COVER` or `ACHIEVEMENT_ICONS`; `204`) | JWT |
@@ -150,7 +159,8 @@ Inside a module: `api` (controllers, DTOs), `service` (business logic), `domain`
 5. `TimeToBeatService` and `MoodService` ask IGDB for missing or old time-to-beat and mood data, for Steam games
    and manual games. Hidden games only get their playtime updated.
 6. After the commit, `LibrarySyncedEvent` starts `AchievementSyncService` and `SpeedrunService` (backlog games only)
-   in the background.
+   in the background. The achievement sync also fetches Steam's global unlock rates with each schema, and sets
+   FINISHED for a game whose ending achievement is unlocked while the user never chose its status.
 
 The frontend polls `GET /api/library/sync-status` until the run ends.