

So your issue sounds is one of disorganization rather than backup or migration.
Use something like WizTree or WinDirStat, which will help you visualize the data on your disk, and hopefully locate your critical files. You’ve got no choice other than to grind it out and get your shit organized.
Once done, migrate your newly organized files onto a new disk. Unless you want to play with weird drivers, I’d recommend you format the new disk as ExFat to maximize compatibility between Linux and Windows.

Elektrek “estimated”, using incomplete data.