Fully agreed - our recommendation is to /not/ run your prod Postgres db yourself, but use one of the many great dedicated options out there - Crunchy Data, Neon, Supabase, or AWS RDS..!
Regardless, you're going to have a much easier time developing your app if your datastore access latency is submillisecond rather than tens of milliseconds.
So that extra trouble might be worth it...
Also, "small scale" means different things to different people. Given the full topic at hand, I would call it "nano scale". Depending upon your specific schema, you can serve tens of thousands of queries per second with a single server on modern hardware, which is way more than enough for the vast majority of workloads.