I've been using Signal for years and my database was getting really bloated with media, attachments, etc but I didn't want to delete it all. I used this and it's incredible:

https://github.com/bepaald/signalbackup-tools

Just make a backup from within signal, copy that backup file to your PC, then run this tool. The commands I used make an HTML webpage that looks just like the signal messenger, along with a way of searching your messages. You can choose different commands to export however you like.

I used:

signalbackup-tools [input] [passphrase] --exporthtml [directory] --split --searchpage --originalfilenames

So while this doesn't help you move off your current messenger, you don't have to worry that your data/messages will be lost in Signal.