fix(worker): capture API route errors in Sentry (#1439)

Author: brendan-kellam

packages/backend/src/api.ts

@@ -1,7 +1,8 @@
 import { PrismaClient, RepoIndexingJobType } from '@sourcebot/db';
+import * as Sentry from '@sentry/node';
 import { hasEntitlement } from './entitlements.js';
 import { createLogger, doesIdpSupportPermissionSyncing, env } from '@sourcebot/shared';
-import express, { Request, Response } from 'express';
+import express, { NextFunction, Request, Response } from 'express';
 import 'express-async-errors';
 import * as http from "http";
 import { ConnectionManager } from './connectionManager.js';
@@ -45,6 +46,11 @@ export class Api {
         app.post('/api/trigger-account-permission-sync', this.triggerAccountPermissionSync.bind(this));
         app.post(`/api/experimental/add-github-repo`, this.experimental_addGithubRepo.bind(this));
 
+        app.use((error: unknown, _req: Request, _res: Response, next: NextFunction) => {
+            Sentry.captureException(error);
+            next(error);
+        });
+
         this.server = app.listen(PORT, () => {
             logger.debug(`API server is running on port ${PORT}`);
         });