one thing i have done recently that definitely didn't work is syncing history from phone->desktop. i haven't gone phone->phone in at least a couple years though--good to hear that that's working better.
on Android you have to do it manually and its by no means easy or intuitive if you are an everyday user. Whatsapp nails this experience on Android with the back up and transfer capability
Note that Whatsapp’s backups are in plaintext and sent to a Google property, while Signal’s backups (even if more cumbersome to set up) are encrypted with a key that only you know.
I hope in 2021 Signal can improve their new transfer method by allowing transfers between Android devices or even ( albeit far more difficult) android and ios