So my very first question, after opening your page, is “what does this get me, if anything, to offset the very large decrease in efficiency vs. the native wireline protocol, given that it’s implemented pretty much everywhere?”

It enables you to use Postgres without the wireline protocol

Feels like they're trying to make something alike PostgREST (and sell it as a service), ie being able to skip backend coding and this manages brokering and permissions for frontends that does most of the job anyhow.

That’s right. You can compare it to Pocketbase, but with PG as storage. It is open source and it’s easy to self host

Does it work with pgbouncer?

Yes, it works without, but it’s recommended in production. You can also use whatever managed PG service you like.