The tally becomes a ledger of its own — and hotseat tables count

Instead of re-scanning every room's log on demand, stats.json now
accumulates beside the room files: each room is remembered at its
highest counted stage (created → started → finished), so boots and
replays reconcile without double-counting, and the tally will survive
any future pruning of old rooms. Finished games contribute their
moves, table-time, and manner of victory exactly once, at the moment
of victory.

And with an accumulator to receive them, hotseat games finally count:
each local game mints an anonymous id, pings "started" with its
player count, tracks its own between-moves clock, and on the final
move reports counts only — commands, minutes, players, win reason.
No names, no moves leave the device. The server dedupes by id, clamps
everything to sane ranges, and the booklet's tally now shows how many
of the games were hotseat tables.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

packages/web/src/net.svelte.ts

@@ -376,6 +376,14 @@ class Net {
     this.send({ type: "stats" });
   }
 
+  /** Anonymous count-only ping so hotseat tables show in the tally. */
+  reportHotseat(report: {
+    id: string; stage: "started" | "finished";
+    players?: number; commands?: number; minutes?: number; winReason?: string;
+  }): void {
+    this.send({ type: "hotseatReport", ...report });
+  }
+
   refreshGames(): void {
     if (this.seats.length > 0) this.send({ type: "myGames", seats: $state.snapshot(this.seats) });
   }