PostgreSQL has 2 memory-related parameters you need to set for larger instances - work_mem and shared_buffers, as these need to be set to a percentage of the VMs memory to utilize it well. However, pretty much every PostgreSQL setup guide names these two values, and on a managed PostgreSQL hosting I'd expect these to be set.

Outside of memory, log_duration, temp_file_limit, a good query plan visualizer and some backup and replication (e.g. PGBackrest and Patroni) are also generally recommended if self-hosting. Patroni doesn't even need an external config store anymore, which is great since you can just run it onto 3-4 nodes and get a high quality HA, easy to manage PostgreSQL cluster.

But those two parameters are pretty much all to have a PostgreSQL process thousands of transactions per second without further tuning. Even our larger DBs hosting simple REST-applications (opposed to ETL/Data warehousing) had to grow quite a lot until further configuration was necessary, if at all.

Checkpointing probably becomes the next issue then, but modern PostgreSQL actually has great logging there -- "Checkpoints occur too frequently, consider these 5 config parameters to look at". And don't touch VACUUM jobs, as a consultant once joked, he sometimes earns thousands of dollars to say "You killed a VACUUM job? Don't do that".

So yeah, actually running PostgreSQL takes a few considerations, but compared to 10 - 15 years ago, you can get a lot with little effort.