Paginate the leaderboard from materialized player ratings

Store each player's leaderboard totals (wins, accumulated points and the
latest display name) on player_rating alongside the Elo rating, updated
in the same transaction as the match, so the board is a single indexed
table query instead of aggregating every participation on each request.

GET /api/leaderboard is now page-number paginated (page/limit) and
returns the page, page count and total, plus the caller's own rank and
page when authenticated; focus=me returns the caller's page directly.
The migration adds the columns, backfills them from the match history
(inserting rows for players from pre-Elo matches at the initial rating)
and replaces the index. backfill_elo rebuilds the aggregates too.

The web page opens on the page containing the signed-in player, marks
their row and adds a numbered footer pager.

server/README.md

@@ -251,8 +251,10 @@ aggregate with `max`, not `sum`.
   seat, game-defined team label (nullable), whether they won, the points
   they scored, the Elo change the match produced (`elo_delta`) and
   game-specific extras (`details` JSON). Unique per `(match, user_sub)`.
-- `player_rating` — current Elo rating per `(user_sub, game_type)`, with
-  the number of rated matches played.
+- `player_rating` — current Elo rating and leaderboard totals per
+  `(user_sub, game_type)`: the rating, matches played, wins, accumulated
+  points and the most recent display name. Kept in sync with the match
+  transaction, so the leaderboard is a single indexed table query.
 
 When a match ends, the engine's result is written transactionally to
 Postgres (once, guarded by a flag on the session); the finished session
@@ -266,10 +268,10 @@ Players carry a chess-style Elo rating per game type
 mean of its members, and the standard formula
 `E = 1 / (1 + 10 ** ((R_opp - R_team) / 400))` with `K = 32` decides how
 many points the match result moves — the same delta for every member of
-a team, zero-sum between the two teams. Ratings update in the same
-transaction as the match result. To recompute every rating from the
-recorded match history (e.g. to backfill matches recorded before ratings
-existed):
+a team, zero-sum between the two teams. Ratings and the leaderboard
+aggregates update in the same transaction as the match result. To
+rebuild every rating and aggregate from the recorded match history (e.g.
+to backfill matches recorded before ratings existed):
 
 ```sh
 .venv/bin/python -m tavolo.platform.backfill_elo \
@@ -292,7 +294,7 @@ All endpoints except `/api/health`, `/api/docs`, `/api/openapi.json`,
 | `GET` | `/api/me/games` | Live games the caller is seated in (waiting lobbies, matches in progress or between hands), newest first, for the lobby's "Continue" list. Finished matches are not included |
 | `GET` | `/api/me/matches` | Cursor-paginated match history with the engine's `result` and per-player Elo deltas (`?limit=&cursor=&game_type=`) |
 | `GET` | `/api/me/ratings` | The caller's Elo rating per game type |
-| `GET` | `/api/leaderboard` | Elo rating, aggregated wins / matches / points per player, sorted by Elo (`?game_type=`) |
+| `GET` | `/api/leaderboard` | Elo rating, wins / matches / points per rated player, sorted by Elo (`?game_type=`, `?page=`, `?limit=`, `?focus=me`). The response carries the requested page, the page count and — when authenticated — the caller's own rank and page; `focus=me` returns the caller's page directly |
 
 ## WebSocket protocol
 
@@ -560,7 +562,7 @@ packages/tavolo-platform/     # game-independent platform (own pyproject + tests
   ├── models.py               # Match / MatchPlayer / PlayerRating (Postgres)
   ├── elo.py                  # chess-style Elo math (1500 start, K=32)
   ├── stats.py                # MatchResult -> Postgres persistence + Elo update
-  ├── backfill_elo.py         # recompute all ratings from the match history
+  ├── backfill_elo.py         # recompute all ratings and aggregates from match history
   ├── store.py                # Redis / in-memory live-session store (+ deadline queue)
   ├── deadlines.py            # connection-independent timeout scheduler
   ├── ws.py                   # WebSocket live-play endpoint (generic envelope)