feat(livestats): per-player killedBy + deathPosition + winner for live standings (#4593)

## Description:

Enriches the admin-bot live-stats snapshot
(`/api/adminbot/game/:id/stats`) with the per-player fields a semi-live
standings board needs, so it can score kills + placement live instead of
waiting for the post-game record.

Per player in `liveStats.players[]`:
- **`killedBy`** — the eliminator's clientID (null while alive /
non-client killer). Invert → live kill points.
- **`deathPosition`** — finishing place at elimination = non-bot players
still standing + 1 (frozen at "last of the then-standing"). Null while
alive → live placement.

The **full roster** is reported (dead players are retained in the client
view), plus top-level **`winner`** (the decided winner's clientID, else
null).

Deterministic / consensus-safe: `killedBy` (stamped at `recordKill`) and
`deathPosition` (stamped in `PlayerExecution`) are pure sim values, so
in-sync clients agree on the majority vote; `winner` is added
server-side in `GameServer.liveStats()` from the winner vote (like the
existing publicID/username/connected enrichment).

## Please complete the following:

- [x] I have added screenshots for all UI updates
- [x] I process any text displayed to the user through translateText()
and I've added it to the en.json file
- [x] I have added relevant tests to the test directory

src/core/game/GameUpdateUtils.ts

@@ -44,6 +44,8 @@ export function diffPlayerUpdate(
     prev.playerType === next.playerType &&
     prev.isAlive === next.isAlive &&
     prev.isDisconnected === next.isDisconnected &&
+    prev.killedBy === next.killedBy &&
+    prev.deathPosition === next.deathPosition &&
     prev.isTraitor === next.isTraitor &&
     prev.traitorRemainingTicks === next.traitorRemainingTicks &&
     prev.inDoomsdayClock === next.inDoomsdayClock &&
@@ -89,6 +91,8 @@ export function diffPlayerUpdate(
   setIfDifferent("playerType", prev.playerType === next.playerType);
   setIfDifferent("isAlive", prev.isAlive === next.isAlive);
   setIfDifferent("isDisconnected", prev.isDisconnected === next.isDisconnected);
+  setIfDifferent("killedBy", prev.killedBy === next.killedBy);
+  setIfDifferent("deathPosition", prev.deathPosition === next.deathPosition);
   // tilesOwned / gold / troops intentionally absent — see EXCEPTION above.
   setIfDifferent("isTraitor", prev.isTraitor === next.isTraitor);
   setIfDifferent(
@@ -157,6 +161,8 @@ export function applyStateUpdate(target: PlayerState, pu: PlayerUpdate): void {
   if (pu.isAlive !== undefined) target.isAlive = pu.isAlive;
   if (pu.isDisconnected !== undefined)
     target.isDisconnected = pu.isDisconnected;
+  if (pu.killedBy !== undefined) target.killedBy = pu.killedBy;
+  if (pu.deathPosition !== undefined) target.deathPosition = pu.deathPosition;
   if (pu.tilesOwned !== undefined) target.tilesOwned = pu.tilesOwned;
   if (pu.gold !== undefined) target.gold = Number(pu.gold);
   if (pu.troops !== undefined) target.troops = pu.troops;