Your only option is to export the database from the desktop app and use third party tools like https://github.com/bepaald/signalbackup-tools https://github.com/

Your only option is to export the database from the desktop app and use third party tools like https://github.com/bepaald/signalbackup-tools https://github.com/bepaald/signalbackup-tools to decrypt the backup. However in my experience this backup does not include all of your messages and as such there is no way to get your chat history out of this walled garden.