Yes! That has been supported for a long while. At least on Android, go to Settings -> Chats -> Chat Backups. Set up a schedule and a passphrase and a folder, and it will export your chats every day.
I do that and then sync that folder with another computer using SyncThing.
They did support it since they released the Files app, as Signal shows. Nothing changed all these years, yet they're now rolling out backups for iOS too, so the technology is already there.