chore(repo): restructure as monorepo with server and client workspaces

- move NestJS app into server/ subdirectory
- add client/ React+TypeScript (Vite) app with Hello World
- update docker-compose to build and run both services
- add root package.json declaring npm workspaces
- update .gitignore to cover node_modules and dist at all depths

server/src/filters/http-exception.filter.ts

@@ -0,0 +1,40 @@
+import {
+  ArgumentsHost,
+  BadRequestException,
+  Catch,
+  ExceptionFilter,
+  HttpException,
+  InternalServerErrorException,
+} from "@nestjs/common";
+import { TraceLogger } from "../common/trace-logger";
+import type { Request, Response } from "express";
+
+@Catch(BadRequestException, InternalServerErrorException)
+export class HttpExceptionFilter implements ExceptionFilter {
+  private readonly logger = new TraceLogger(HttpExceptionFilter.name);
+
+  catch(exception: HttpException, host: ArgumentsHost): void {
+    const ctx = host.switchToHttp();
+    const request = ctx.getRequest<Request>();
+    const response = ctx.getResponse<Response>();
+    const status = exception.getStatus();
+    const body = exception.getResponse();
+
+    const cause = (exception as unknown as { cause?: Error }).cause;
+    const causeMessage = cause ? ` | cause: ${cause.message}` : "";
+    const message = `${exception.message}${causeMessage}`;
+
+    if (status >= 500) {
+      this.logger.error(
+        `[${request.method} ${request.url}] ${status} — ${message}`,
+        cause?.stack ?? exception.stack,
+      );
+    } else {
+      this.logger.warn(
+        `[${request.method} ${request.url}] ${status} — ${message}`,
+      );
+    }
+
+    response.status(status).json(body);
+  }
+}