It "works," but... operator beware.
I'm also not exactly sure if you'll get full stats out of a replica.
This is one of the biggest PITAs with hosted Postgres - you can't just use whatever extensions you want, or indeed whatever version of those extension. Invariably AWS and Azure (presumably GCP too, I haven't used it) have only the most popular extensions available, and invariably woefully outdated versions.
Now of course your statement about pg_stat_monitor is correct, too. But you missed when you questioned Peter since he was talking about something different.
Fun fact: Peter Geoghegan is a PostgreSQL major contributor per https://www.postgresql.org/community/contributors/, pretty sure he's a committer as well.
Longer term we're exploring the ability to bring your own and already have some thoughts on how to make that possible.