feat(api): add global error handler with typed error classes

- Add AppError base class, ValidationError (400), NotFoundError (404)
- Add central error middleware in app.ts
- Remove inline safeParse error handling from controllers
- Replace plain Error throws with NotFoundError in gameService

apps/api/src/services/gameService.ts

@@ -8,8 +8,8 @@ import type {
   AnswerSubmission,
   AnswerResult,
 } from "@glossa/shared";
-
 import { InMemoryGameSessionStore } from "../gameSessionStore/index.js";
+import { NotFoundError } from "../errors/AppError.js";
 
 const gameSessionStore = new InMemoryGameSessionStore();
 
@@ -39,7 +39,6 @@ export const createGameSession = async (
 
       const optionTexts = [correctAnswer.targetText, ...distractorTexts];
       const shuffledTexts = shuffle(optionTexts);
-
       const correctOptionId = shuffledTexts.indexOf(correctAnswer.targetText);
 
       const options: AnswerOption[] = shuffledTexts.map((text, index) => ({
@@ -64,6 +63,7 @@ export const createGameSession = async (
 
   return { sessionId, questions };
 };
+
 const shuffle = <T>(array: T[]): T[] => {
   const result = [...array];
   for (let i = result.length - 1; i > 0; i--) {
@@ -81,13 +81,13 @@ export const evaluateAnswer = async (
   const session = await gameSessionStore.get(submission.sessionId);
 
   if (!session) {
-    throw new Error(`Game session not found: ${submission.sessionId}`);
+    throw new NotFoundError(`Game session not found: ${submission.sessionId}`);
   }
 
   const correctOptionId = session.answers.get(submission.questionId);
 
   if (correctOptionId === undefined) {
-    throw new Error(`Question not found: ${submission.questionId}`);
+    throw new NotFoundError(`Question not found: ${submission.questionId}`);
   }
 
   return {