Apple ID vs iCloud ID

I have an iPad 2 from years ago (which I set up using a work email address) and an iPhone SE from last year with a new Apple ID using my personal email address. I've just bought myself a new iPad so I can use Teams. I've set the new iPad up and it shares the same Apple ID as my iPhone SE. All good.

However, I cannot reset the iPad 2 to wipe it clean. I've signed out on it and signed in again successfully with my current Apple ID without any problem... but still I cannot reset it. It keeps asking for my old Apple ID... (same name, just different email) which I can see in the settings for iCloud.

I've been to appleid.apple.com to change my email address but cannot sign in with my old Apple ID. I used 'Recover your Apple ID' and put in my details... and it says "This Apple ID is not valid or not supported." I clicked on the link where it says "If you forgot your Apple ID, you can look it up." and enter my first name, last name and old work email address and it come back with 'No Apple ID found'.

If I go into Settings, iCloud shows my old Apple ID with work email address yet iTunes & App Store shows the current Apple ID I've been using since I got my iPhone SE. I can't even turn off 'Find My iPad' 'cos it refers to my old Apple ID which Apple says 'No Apple ID found' (even though I know the darn password for it).

I don't understand why signing out/signing in with my current Apple ID on the old iPad hasn't changed the iCloud details from my old Apple ID... and I don't understand why they should be separate.

How do I wipe it? I seem to be going round in circles.