Get into iPad

Can you use "Find My" to locate the 2FA device (presumably an iPhone)?  If you're using iCloud to find a device you shouldn't need 2FA to do this.
(Of course "Find My" iPhone has to have been set up in advance)
Accessing the iPad without a 2FA device without wiping isn't supported AFAIK :(

I'm thinking that you would have to contact Apple support in that case.

https://getsupport.apple.com/?caller=psp

Sorry - I meant to add - 'wiping' is not a problem. A hard factory reset is fine

Ok, did you try to put it in recovery mode and then connect it to a PC with iTunes running?

Trouble is, currently, I don't have
a. iTunes
b. Windows

MacOS (unsurprisingly) also supports iTunes, but if there is no time pressure to wipe and reset the device perhaps ask again when you have everything available?

tbh I asked here in order to avoid jumping through all the hoops of what the device is seemingly asking me to do. Is there really no hardware reset?

Catch22, yes, but you need the passcode to activate it and confirm (safety measure).

So, what's going to happen when I do open iTunes? All I know is the Apple ID and corresponding password. I have no other devices.

You'll have the iPad in Recovery mode and iTunes connecting it to Apple.
iTunes then allows you to bypass the protection on factory resetting

Passcode will be removed and you specify a replacement

The AppleID might help you recover data if there's an iCloud backup of the device with those credentials (or at least give you that option)

https://support.apple.com/en-gb/HT211078

Ah right thanks. Next thing is I don't have an Apple cable. Unless this model uses a generic USB (not that I can tell which model it is)?

Next to the button the socket will either be around 2cm (the older iPad cable that's a little trickier to source these days) or short. The latter will either fit a USB-C plug or more likely a Lightning connector, you can pick these up for a £ or two (or for pennies in boxes of mixed cables!) - or borrow off anyone with an iPhone more that a few years old!

So far, appears to be a total waste of time

a. got Windows
b. borrowed cable
c. installed iTunes

all that happens is the same thing - 2FA is offering to send a code to another device (which i don't have)

UPDATE - *something* is happening...

That is what you needed (cabling) - did you put the iPad into recovery mode?

You should only see 2FA offered if you're recovering the passcode. Not to wipe.

However iTune routinely asks for passcode when you connect a device via USB .

Shouldn't in recovery mode though.

Hoping "something happening" is more promising!

I was under the impression that I'd need to create an Apple ID to enable installation of software (I need an ssh server) but maybe that's not correct? Anyhow, the device won't allow me to create one

What stage are you at in the process?
Is the device wiped yet?

iTunes sometimes takes longer that the Recovery Mode timeout to download and install the reset tools so if Recovery Mode stops just allow iTunes to complete the download, then put it back into Recovery Mode and try again.

Looks like it's recovered yes. I can log in with a passcode. Won't allow me to create an Apple ID, but maybe I don't need it

You can create an Apple ID here: https://appleid.apple.com/account

Then configure the iPad using that (new) Apple ID.

Do I actually need it though? And btw, I suspect the problem is that the iPad is associated with a different id (my late father's) that is locked

Thanks. tbh I was already wary about playing in Apple's walled garden, which is why I'd never buy an Apple device, but since they won't even let me into their garden, it can probably go to landfill.