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.

src/main/resources/db/migration/V14__status_change_log.sql

@@ -0,0 +1,30 @@
+-- Every status a library game ever had, for "finished per year" and the Pile of Shame trend. Written by a trigger,
+-- so no code path (entity save, bulk update, native insert) can forget it. The past is not known: the log starts
+-- on the day of this migration.
+CREATE TABLE user_game_status_change (
+    id          BIGSERIAL   PRIMARY KEY,
+    user_id     BIGINT      NOT NULL,
+    appid       BIGINT      NOT NULL,
+    -- NULL: the game came into the library with to_status.
+    from_status VARCHAR(16),
+    to_status   VARCHAR(16) NOT NULL,
+    -- user_game.status_set_by_user after the change: false for the sync and for Core's own FINISHED.
+    by_user     BOOLEAN     NOT NULL,
+    changed_at  TIMESTAMPTZ NOT NULL DEFAULT NOW(),
+    FOREIGN KEY (user_id, appid) REFERENCES user_game (user_id, appid) ON DELETE CASCADE
+);
+CREATE INDEX idx_status_change_user_time ON user_game_status_change (user_id, changed_at);
+
+CREATE FUNCTION log_user_game_status() RETURNS TRIGGER AS $$
+BEGIN
+    INSERT INTO user_game_status_change (user_id, appid, from_status, to_status, by_user)
+    VALUES (NEW.user_id, NEW.appid, CASE WHEN TG_OP = 'UPDATE' THEN OLD.status END, NEW.status,
+            NEW.status_set_by_user);
+    RETURN NULL;
+END;
+$$ LANGUAGE plpgsql;
+
+CREATE TRIGGER user_game_status_insert AFTER INSERT ON user_game
+    FOR EACH ROW EXECUTE FUNCTION log_user_game_status();
+CREATE TRIGGER user_game_status_update AFTER UPDATE OF status ON user_game
+    FOR EACH ROW WHEN (OLD.status IS DISTINCT FROM NEW.status) EXECUTE FUNCTION log_user_game_status();

src/main/resources/db/migration/V15__game_genres.sql

@@ -0,0 +1,4 @@
+-- IGDB genre names (e.g. "Role-playing (RPG)") per game, for the stats page. Filled with the moods; the next
+-- library sync asks IGDB for every game again, so the column gets filled.
+ALTER TABLE game_mood ADD COLUMN genres VARCHAR(64)[] NOT NULL DEFAULT '{}';
+UPDATE game_mood SET checked_at = TIMESTAMPTZ 'epoch';

src/main/resources/db/migration/V16__backlog_snapshot.sql

@@ -0,0 +1,25 @@
+-- The size of each user's pile per day (Europe/Berlin), for the Pile of Shame trend. The nightly sync writes one row
+-- per user with listed games; the past cannot be rebuilt, so the trend starts with the row of the migration day.
+CREATE TABLE backlog_snapshot (
+    user_id         BIGINT  NOT NULL,
+    day             DATE    NOT NULL,
+    backlog_games   INTEGER NOT NULL,
+    never_played    INTEGER NOT NULL,
+    -- Normal time to beat of the backlog games IGDB knows; it also grows when IGDB learns new times.
+    backlog_minutes BIGINT  NOT NULL,
+    listed_games    INTEGER NOT NULL,
+    PRIMARY KEY (user_id, day)
+);
+
+INSERT INTO backlog_snapshot (user_id, day, backlog_games, never_played, backlog_minutes, listed_games)
+SELECT ug.user_id, (NOW() AT TIME ZONE 'Europe/Berlin')::date,
+       COUNT(*) FILTER (WHERE ug.status = 'BACKLOG'), COUNT(*) FILTER (WHERE ug.playtime_minutes = 0),
+       COALESCE(SUM(t.normally_minutes) FILTER (WHERE ug.status = 'BACKLOG'), 0), COUNT(*)
+FROM user_game ug LEFT JOIN game_time_to_beat t ON t.appid = ug.appid
+WHERE ug.removed_at IS NULL AND ug.hidden_at IS NULL
+GROUP BY ug.user_id;
+
+-- When the current Steam account's first sync ran: the games of that sync are the import, no "added" in the trend.
+-- The accounts of today count from the migration on, like the status history.
+ALTER TABLE user_steam_sync ADD COLUMN history_since TIMESTAMPTZ;
+UPDATE user_steam_sync SET history_since = NOW() WHERE history_steam_id IS NOT NULL;

src/main/resources/db/migration/V17__finished_at_estimate.sql

@@ -0,0 +1,5 @@
+-- For a FINISHED or COMPLETED game: when the user unlocked its ending achievement (the rule of EndingAchievement).
+-- "Finished per year" counts the game in that year, before the status history (V14): a game finished by hand or by
+-- Core long after its ending, e.g. when the library is first set up, still counts in the right year. Filled by the
+-- nightly job; NULL when the game has no ending achievement, it is not unlocked, or Steam sent no unlock time.
+ALTER TABLE user_game ADD COLUMN finished_at_estimate TIMESTAMPTZ;