Use spawn tile for name placement during spawn phase

Names now follow the player's currently-selected spawn tile each tick
instead of going through placeName, which read a cluster bounding box
that only refreshed every cluster-calc cycle and was further throttled
to every other tick. Adds placeSpawnName and switches the spawn-phase
branch in GameRunner to use it.

src/client/hud/NameBoxCalculator.ts

@@ -13,6 +13,37 @@ export interface Rectangle {
   height: number;
 }
 
+// Spawn region diameter (see getSpawnTiles in SpawnExecution — euclidean
+// radius 4). Used to size spawn-phase names directly off the spawn tile,
+// instead of waiting on cluster recomputation.
+const SPAWN_REGION_DIAMETER = 8;
+
+/**
+ * Place a player's name during the spawn phase using their currently-selected
+ * spawn tile. Tracks re-rolls immediately, since spawnTile updates the same
+ * tick the player picks a new location.
+ */
+export function placeSpawnName(game: Game, player: Player): NameViewData {
+  const spawnTile = player.spawnTile();
+  if (spawnTile === undefined) {
+    return { x: 0, y: 0, size: 0 };
+  }
+  const fontSize = calculateFontSize(
+    {
+      x: 0,
+      y: 0,
+      width: SPAWN_REGION_DIAMETER,
+      height: SPAWN_REGION_DIAMETER,
+    },
+    player.displayName(),
+  );
+  return {
+    x: Math.ceil(game.x(spawnTile)),
+    y: Math.ceil(game.y(spawnTile) - fontSize / 3),
+    size: fontSize,
+  };
+}
+
 export function placeName(game: Game, player: Player): NameViewData {
   const boundingBox =
     player.largestClusterBoundingBox ??