Edit:

I'm building a new application for the openstore: Signal UT, which will be a custom version of signal-desktop for Ubuntu Touch. I've already succeeded to build an initial .click package of signal-desktop for Ubuntu Touch  with basic tweaking to have a more acceptable scale and have the keyboard working. I've made scripts to build it automatically. Currently it is based on a reuse of the binaries from https://snapcraft.io/signal-desktop . But it does not require to use snap to work, it's a standalone click package (that we'll be able to publish openstore later).
https://github.com/pparent76/SignalUT
The app is currently not responsive (but I plan to work on it):
- You can reduce the left menu to it's minimal size, as a temporary workaround
 
- The keyboard will display on top of the textedit, so you won't see what you type
 
- [EDIT] Somehow the "enter" and "back" buttons of the keyboard do not work after starting the app, but locking and unlocking the phone with Signal in foreground will solve it. (Probably and Xmir problem)
 
- You should be able to fine tune zoom by plugin in a keyboard and use the shortcuts Ctrl+= & Ctrl+- (untested)
 
But it is already usable to consult messages, and send small messages (in a sub-optimal way)
What also works or kind of works:
- Sending Audio messages, and listening to them (seems to work quite well)
 
- Audio calls (and it's possible to see video from the other person but internal camera does not work), call quality untested.
 
- Receiving non-Ut desktop notifications when keeping app in background (even when the phone is suspended)
 

WARNING: This is experimental, use at your own risks. The app currently needs to run unconfined. It contains binaries, that are free software but that I've not compiled personally (coming from snapcraft.io ) and that I have not checked. I do not take responsibility in case of any problem
Knowing that, if you want to be a tester, I'd be glad to get feedback from testers to know if it runs on other phones. So you will find a pre-built .click package here ( ONLY RUN ON NOBLE (24.04) ) :
https://github.com/pparent76/SignalUT/releases/tag/FirstRelease