fix(db): cap the pg connection pool, configurable per environment

lib/db/client.ts

@@ -11,8 +11,19 @@ function createPrismaClient() {
     throw new Error("DATABASE_URL environment variable is required");
   }
 
+  // Without an explicit cap, pg.Pool opens up to 10 connections per process and
+  // the adapter was only given the connection string. On serverless every warm
+  // instance builds its own pool, so two of them already exceeded the 15
+  // connections of Supabase's free session pooler — surfacing as Prisma's
+  // "Can't reach database server", which reads like an outage rather than an
+  // exhausted pool. The cap is per-environment: small on Vercel, a bit higher
+  // on the worker, which is a single long-lived process.
   return new PrismaClient({
-    adapter: new PrismaPg(databaseUrl),
+    adapter: new PrismaPg({
+      connectionString: databaseUrl,
+      max: Number(process.env.DB_POOL_MAX ?? 3),
+      idleTimeoutMillis: 10_000,
+    }),
   });
 }