In my (minor) experience Timescale works fine. The developer experience is good and it is very convenient to be able to JOIN against your hypertables. My only real complaints are operational (no logical replication, normal postgres update complaints), but man Clickhouse is really slick. I wrote some small reviews of the two in my submission history if you want a bit more detail.

I would just run both and decomission the old one when a) all data is migrated, b) old data is no longer relevant and can be archived

Worked on peerdb. If you're able to batch changes on your end & push to both postgres & clickhouse, do that. Only move to peerdb when you know you need cdc