We have deployed OtterTune for on-prem databases (baremetal, containers). But we are not offering that to everyone right now because organizations manage their configurations for these deployments in a bunch of different ways (Github actions, Chef/Puppet, Terraform). The nice thing about RDS is that they have a single API for updating configurations (
https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_...).
As for the Postgres-derivates that you mentioned (Timescale, Citus), we have not tested OtterTune for them yet. But there is no reason they shouldn't also work because they expose the same metrics API (pg_stat_database) and config knobs. There are just way more people using Postgres (RDS, Aurora), so we are focusing on them right now.