feat(library): add stats page data and pile trend

Log every status change with a trigger, so no code path can miss it.
Store IGDB genres with the moods. Write a pile snapshot per user each
night. The sync moves an untouched pile game with new playtime to
PLAYING in one guarded update, so a status the user picks wins.
Old finished games get their year from the ending achievement.
GET /api/library/stats serves the groups; the public profile shows
only the groups in the profile ticket.

readme.md

@@ -43,6 +43,15 @@ To Be Played is split into three repositories:
   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
   lists hidden games with `hidden=true`.
+- **Stats**: `UserStatsService` builds the numbers of the stats page per group, so every page asks only for the
+  groups it shows: totals and statuses; the pile (time to beat, weeks "at your pace" of the last 90 days, years of
+  40-hour weeks, oldest unplayed game); most played and most loyal game (most months with playtime); top IGDB genres
+  and moods; moon trips (Apollo 11, 195.3 h), longest day, share under one hour; finished games per year (from the
+  status history); the Pile of Shame trend (90 days of `backlog_snapshot`, plus "this month: added / done", where the
+  first sync of a Steam account is no "added", see `user_steam_sync.history_since`). Every number counts only listed games.
+- **Status history**: a database trigger logs every status change of a library game in `user_game_status_change`
+  (old and new status, time, whether the user chose it), whatever code path made it. It starts with V14; older
+  changes are not known.
 - **Wishlist**: synced from Steam with store price and discount.
 - **Broken image repair**: the frontend reports a Steam cover or achievement icon that does not load. At 01:30
   (Europe/Berlin) a job checks up to 200 reports. A cover that loads again is left alone; else the store's hashed
@@ -53,7 +62,8 @@ To Be Played is split into three repositories:
   feature is off and the rest works.
 - **Public profile data**: totals, status counts, games in progress and finished games with rating, perfect games
   and average completion. Readable only
-  with a profile ticket issued by Auth. Never returns notes, priority or the Steam ID.
+  with a profile ticket issued by Auth. Never returns notes, priority or the Steam ID. `stats` holds only the stat
+  groups the user shares (the ticket's `profileStats` claim, set in Auth); none by default.
 
 ## Authentication
 
@@ -78,6 +88,7 @@ accepted only by `GET /api/public/profiles/library` in the `X-Profile-Ticket` he
 | `POST` | `/api/library/sync` | JWT |
 | `POST` | `/api/library/broken-images` (`{appid, kind}`, kind `COVER` or `ACHIEVEMENT_ICONS`; `204`) | JWT |
 | `GET` | `/api/library/picker?maxMinutes=&mood=&count=&exclude=` | JWT |
+| `GET` | `/api/library/stats?groups=` (`OVERVIEW`, `PILE`, `TOP_GAMES`, `TASTE`, `HABITS`, `FINISHED`, `TREND`; none = all) | JWT |
 | `GET` | `/api/library/achievements/summary` | JWT |
 | `GET` | `/api/library/sync-status`, `/summary`, `/activity`, `/wishlist`, `/steam-profile`, `/games-count` | JWT |
 | `GET` | `/api/public/profiles/library` | profile ticket |
@@ -152,12 +163,16 @@ Inside a module: `api` (controllers, DTOs), `service` (business logic), `domain`
    `POST /api/library/sync` starts one at once, but at most every 60 seconds (else `429` with `Retry-After`).
 2. A nightly job (23:55, Europe/Berlin) syncs every account used in the last 14 days, one after the other. A
    request without a `steamId` claim (the user unlinked the Steam account in Auth) takes the user out of it.
+   Afterwards it writes every user's pile size of the day to `backlog_snapshot`, also for users without Steam, and
+   dates finished games by the unlock of their ending achievement
+   (`FinishedEstimateService`, `user_game.finished_at_estimate`).
 3. `LibrarySyncWorker` runs in the background. `user_steam_sync` lets only one run per user start.
 4. The worker loads the wishlist and the owned games from Steam. It updates `steam_game` and `user_game`, adds
    the playtime growth of the day to `user_game_playtime_day`, and soft-deletes Steam games the user no longer
-   owns. When Steam returns no games, the library stays as it is.
-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.
+   owns. A BACKLOG game with new playtime becomes PLAYING, unless the user chose its status. When Steam returns no
+   games, the library stays as it is.
+5. `TimeToBeatService` and `MoodService` ask IGDB for missing or old time-to-beat, mood and genre 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. 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.