Mac Mini M1 (8g 250gb) - Transferring internal disk programmes to external Thunderbolt 3 1TB drive

If I get your question correctly, and it's a bit hard cause the text is displayed in a weird way (at least in Safari on my machine), you want to move the non-essential data to external drive, right? And when it comes to Logic Pro X and its Sound Library, it's a way to go, I'd say. This way you'd free some 60+ GB of disk space on your built-in (system) HD.

To achieve this goal, you'll need to: 1) Format the external drive either as "APFS" (preferred for latest macOS, i.e. 11 and 12) or "MacOS Extended Journaled" (also known as "HFS+" file system), and 2) Use Sound Library Manager (Logic Pro X > Sound Library > Relocate Sound Library) to move Logic's sound library content to external drive.

Moving your other data is beyond the scope of this discussion board, I'd say. And it also depends on such factors as what other software is in use, what kind of data do you want to move from your system HD to external, and so on.

However, before making any non-reversible decisions regarding your data, please be advised that LPX Sound Library cannot be moved to the same external HD that is used for Time Machine backups. That's in case you're also planning to use Thunderbolt drive for TM backups. It's recommended to use a dedicated separate drive for Time Machine stuff.

macOS has a utility for disk management, i.e. Disk Utility: normally found in Applications > Utilities folder

Just connect your external HD, wait for it to be mounted (you'd see it on desktop and will be able to open and browse its contents) and launch that utility. When Disk Utility opens, you'll see a list of mounted drives on the left side of its window.

Your Thunderbolt drive should appear under "External". Select the drive (drive itself and not the exFAT partition on it) and then click on a button on top of Disk Utility window, which says "Erase".

This should open a drop-down dialogue where you'll be able to select the format type (APFS or MacOS Extended Journaled, etc etc), partition table (use GUID), and type in the new partition name. That's it in a nutshell.

Needless to say, formatting a drive can lead to data being lost, so the usual disclaimer applies: if you have any valuable data on the HD being formatted (or otherwise manipulated using Disk Utility), back up everything to another HD or USB drive first.