Just want to make sure we are on the same page. Some verbage you are using is causing some confusion for me. So I need clarification.

Are you asking if you can export all of your files onto an external hard drive. Do a clean install of a new Linux distro to wipe away any Linux Mint shenanigans. Then import all the files from the external hard drive back onto the fresh Linux installation with a new distro?

If so, yes, no problem. Easy peasy lemon squeezy. Lots of different ways to do this.

If no, please elaborate further to help me understand your inquiry.

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I have done a timeshift and yes it uses BTRFS.

If you are using timeshift for a backup solution it really is intended for the root file system. Even though there is still an option to include the home directory. It can just get messy over time and eat up a lot of hard drive space if you don't frequently remove your old backups.

My suggestion in your situation is to use Restic for your home directory contents. Which has all of your user files and some of your desktop environment configurations. Timeshift for your root directory and everything else on your system. Keep them separated.

https://restic.net/

Then you could just keep restic exported encrypted external backups of your home directory contents with all your stuff in it. Gracefully use restic to import and restore backups back into your newly installed Linux distro. Quickly and efficiently without a fuss.

Then again you also have the tried and true lazy route. Which sometimes doesn't always go as planned with very large transfers.

Open up the file manager, drag, and drop the files to the external hard drive at the mounted location. Install the new Linux distro. Open up the file manager again. Then copy back over the files onto the new system. Good to go.