fix: timer now in sync with backend

src/app/pages/game/game.facade.ts

@@ -13,6 +13,7 @@ import { GameStreamService } from '../../services/game-stream.service';
 export class GameFacade implements OnDestroy {
   gameId = '';
   game: GameFull | null = null;
+  clockSyncedAt = 0;
   errorMessage = '';
   moveInput = '';
   fenInput = '';
@@ -119,6 +120,7 @@ export class GameFacade implements OnDestroy {
         next: (state) => {
           if (this.game) {
             this.game = { ...this.game, state };
+            this.clockSyncedAt = Date.now();
             this.updateGameCompletion();
           }
           this.moveInput = '';
@@ -207,6 +209,7 @@ export class GameFacade implements OnDestroy {
       .subscribe({
         next: (game) => {
           this.game = game;
+          this.clockSyncedAt = Date.now();
           this.loading = false;
           this.updateGameCompletion();
           this.startStreaming();
@@ -232,6 +235,7 @@ export class GameFacade implements OnDestroy {
   private applyStreamEvent(event: GameStreamEvent): void {
     if (event.type === 'gameFull') {
       this.game = event.game;
+      this.clockSyncedAt = Date.now();
       this.boardSelection = this.boardSelectionService.clearSelection();
       this.updateGameCompletion();
       this.tryMakeBotMove();
@@ -241,6 +245,7 @@ export class GameFacade implements OnDestroy {
     if (event.type === 'gameState' && this.game) {
       const moveCountBefore = this.game.state.moves.length;
       this.game = { ...this.game, state: event.state };
+      this.clockSyncedAt = Date.now();
       this.updateGameCompletion();
       if (event.state.moves.length !== moveCountBefore) {
         this.boardSelection = this.boardSelectionService.clearSelection();