Add Game::process_throw to centralize throw→simulation→scoring→state flow.

Remove dead room_tx field, simplify add_player, and rename end_ends_or_continue.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

@@ -24,7 +24,13 @@ pub struct Game {
     stones_red: u8,

@@ -42,43 +48,31 @@ impl Game {
             stones_red: STONES_PER_TEAM,

@@ -109,4 +97,1 @@
-        }
-    }
-
     pub fn can_start(&self) -> bool {

@@ -183,4 +189,1 @@
-        self.score_end_internal(true);
-    }
-
     fn score_end_internal(&mut self, force: bool) {

@@ -112,1 +110,3 @@
-        }
+    if try_join_room(&room).await.is_err() {
+        let err = serde_json::to_string(&ServerMessage::Error {
+            message: "Room is full".to_string(),

@@ -188,0 +221,4 @@
+                        .process_throw(&player_id, broom_x, broom_y, weight, curl, friction)
+                    {
+                        Ok(ThrowOutcome {
+                            trajectory,

@@ -188,0 +222,4 @@
+                    {
+                        Ok(ThrowOutcome {
+                            trajectory,
+                            end_scored,

@@ -133,3 +132,4 @@
+    activeStonePos: DrawableStone | null
   }) => {
     ctx.clearRect(0, 0, window.innerWidth, window.innerHeight)
 

@@ -29,3 +35,4 @@
+
 export interface ClientThrowMessage {
   type: 'throw'
   broom_x: number

@@ -17,3 +5,4 @@
+import { GameModel } from './game-model'
 
 export function startGame(): void {
   const app = document.querySelector<HTMLDivElement>('#app')!

@@ -259,2 +172,2 @@
-    if (gameState.myTeam !== gameState.turnTeam || gameState.animating || gameState.phase !== 'playing') return
-    sendThrow(broom.x, broom.y, velocity.getWeight(), curls.getSelected(), friction.getFriction())
+    if (!model.isMyTurn) return
+    sendThrow(model.broom.x, model.broom.y, velocity.getWeight(), curls.getSelected(), friction.getFriction())

@@ -0,0 +72,4 @@
+  }
+
+  tick(now: number): DrawableStone | null {
+    if (!this.state.animating || this.activePath.length <= 1) {

@@ -0,0 +99,4 @@
+    const y = p0[1] + (p1[1] - p0[1]) * t
+    const dx = t2[0] - t0[0]
+    const dy = t2[1] - t0[1]
+    const rotation = Math.atan2(dy, dx) * 2