Database connection issues with 3-4k users

Question

I have two apps connected to the Postgres database, each with a connection pool size of 20.

const db: any = {
  type: 'postgres',
  url: DATABASE_URL,
  entities: [`${__dirname}/entity/*.entity{.ts,.js}`],
  migrations: [`${__dirname}/migrations/*{.ts,.js}`],
  logging: 'all',
  extra: {
    max: 20,
    min: 5,
    idleTimeoutMillis: 30000,
    connectionTimeoutMillis: 10000
  }
};

But running a stress test with k6 browser, I get this error with around 3-4k users calling 3 endpoints, 1 of them being cache 95% of the time:

Timeout exceeded when trying to connect [
Apr 06 23:23:03
'Error: timeout exceeded when trying to connect
' +
Apr 06 23:23:03
' at Timeout._onTimeout (/app/node_modules/pg-pool/index.js:205:27)
' +
Apr 06 23:23:03
' at listOnTimeout (node:internal/timers:594:17)
' +
Apr 06 23:23:03
' at process.processTimers (node:internal/timers:529:7)',
Apr 06 23:23:03
'ExceptionsHandler'
Apr 06 23:23:03
]
Apr 06 23:23:03
2025-04-07T03:22:55.583Z [error] - timeout exceeded when trying to connect

That makes the API and database unresponsive.