In 57 years of owning, operating and fixing construction equipment of all kinds, including owning a sizeable number of Cats (including a Cat 12), I have never previously seen a Cat oil clutch stuck. Just goes to show, you learn something new every day, no matter how old you get.
I can see where water or serious amounts of moisture has been in the oil though - and where you get moisture, you get corrosion.
FWIW, I would have drained the clutch compartment and refilled it with a 50/50 mix of ATF and diesel. This is a mix that informed equipment restorers use to unstick rusted bores on engines. It works, it just needs a bit of time to soak in.
For clutch parts, try John Parks at TractorParts.com (General Gear & Machine, Boise, ID.) John specialises in supplying a wide range of steering clutch plates and flywheel clutch plates. I did not see a listing for Cat 12 flywheel clutch plates on his site, but he would certainly be worth a call.
FWIW, the Cat 12 oil clutch is generally an exceptionally long-lived clutch, it's not unusual to have them last for 20,000 hrs.
https://www.tractorparts.com/