feat: NCWF-5/6/7/8/9 chess analysis page and engine integration

- NCWF-5: scaffold /analysis route with ChessBoard viewer and navigation
- NCWF-6: FEN / PGN / Game-ID input form with depth selector
- NCWF-7: extend GameApiService with analyzePosition(); add AnalysisService
  with game-wide annotation pipeline; proxy /api/analysis -> :8087
- NCWF-8: EvalTimelineComponent — SVG win-chance chart per ply
- NCWF-9: AnnotatedMoveListComponent — quality labels (!! ! ?! ? ??)
  derived from win-chance delta

Also fix pre-existing app.spec.ts failure (missing provideHttpClient).
Apply project-wide prettier formatting pass.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/app/services/game-api.service.ts

@@ -7,8 +7,9 @@ import {
   GameState,
   GameStreamEvent,
   LegalMovesResponse,
-  PlayerInfo
+  PlayerInfo,
 } from '../models/game.models';
+import { AnalysisRequest, AnalysisResponse } from '../models/analysis.models';
 import { StreamHandlerService } from './stream-handler.service';
 
 @Injectable({ providedIn: 'root' })
@@ -28,11 +29,11 @@ export class GameApiService {
     const playerColor = Math.random() > 0.5 ? 'white' : 'black';
     const playerInfo: PlayerInfo = {
       id: `player-${Date.now()}`,
-      displayName: 'You'
+      displayName: 'You',
     };
     const botInfo: PlayerInfo = {
       id: `bot-${difficulty}`,
-      displayName: `Bot (${difficulty})`
+      displayName: `Bot (${difficulty})`,
     };
 
     const payload =
@@ -56,7 +57,9 @@ export class GameApiService {
     if (square) {
       params = params.set('square', square);
     }
-    return this.http.get<LegalMovesResponse>(`${this.apiBase}${this.apiPath}/${gameId}/moves`, { params });
+    return this.http.get<LegalMovesResponse>(`${this.apiBase}${this.apiPath}/${gameId}/moves`, {
+      params,
+    });
   }
 
   importFen(fen: string): Observable<GameFull> {
@@ -75,6 +78,10 @@ export class GameApiService {
     return this.http.post<void>(`${this.apiBase}${this.apiPath}/${gameId}/draw/offer`, {});
   }
 
+  analyzePosition(request: AnalysisRequest): Observable<AnalysisResponse> {
+    return this.http.post<AnalysisResponse>(`${this.apiBase}/api/analysis/position`, request);
+  }
+
   private resolveWsBase(): string {
     if (this.wsBase) {
       return this.wsBase;