I'm using both messaging services on my Pinephone (I'm on Manjaro Phosh). Telegram is the desktop version I believe, so mobile only features don't work on there, but overall it works very well. Even voice calls are fine with a headset. I had registered a Telegram account ages ago on another phone, so I didn't have to register a new account, but I believe it's possible. There is no need for scanning a code or anything. I just had to type in my number and then received a confirmation code via SMS, so I think setting up a new account works the same way.
Signal is not as easy. I'm using
Axolotl in server mode with Firefox for the front end which works for the basics. A big missing feature is group support though, Signal's new version of groups is not yet supported. Apparently Signal now forces users to upgrade old groups which effectively shuts you out from group messaging. Apart from Axolotl there is an effort to make
another Signal client though.
Edit: I also had a Signal account before. But
here it seems like it might be possible to set up a new Account with Axolotl as well. Seems to be the same process as with Telegram. At least worth a try I guess.
Edit 2: Official Telegram documentation suggests otherwise, seems I was wrong about registration with the desktop app. Anbox still might be an option for setting up Telegram as well as Signal initially.