Why can't you log into iCloud? unless somethings changed in the past year or something broke between ios 6 and 10, it should work. I'm still signed into my iPad 2 running iOS 6 (granted, iirc the root cert expired a bit ago so you need to update that). the 2fa is also a bit weird, you have to input the code after your password (eg: if your password is password123 and the code is 789 you'd submit password123789)
I think that might be a thing with apples Advanced Data Protection if you have it enabled, which is understandable since the software needs to know how to un-encrypt the data. If you don't have that enabled, then ignore this and assume apple decided to kill a whole lot of devices (particularly their macs, I know a surprising amount of people still on 10.15)
