I dismantled the damaged fob again just to check something. I realised I hadn't checked whether the contact on the PCB had been permanently forced into the ON position, but everything seems fine. All three plastic tabs are sitting well proud of the contacts, and all three contacts operate normally, clicking down and up cleanly when pressed directly. The key is working normally and the doors-open and doors-closed buttons function normally. Hard to check the boot-open button because (and I actually didn't realise this until now) if you are standing in front of the boot with your key on you, it unlocks itself automatically, but it seems OK. I'll just have to wait till Sunday or Monday to see whether the battery is still draining.
If all is well I might buy a new shell (thanks Ian) just for the aesthetics. Interesting that these come with colour co-ordination, but apparently without the MG logo. Maybe it's a trademark thing.
I'm still struggling with the Digital Key. I select my car and it says the Bluetooth is disconnected, with a blue button on the right saying "connect". When I click that I get a pop-up headed "Apply" that says "please authorise the Location/Nearby devices permission". Buttons for No and Yes.
I click on Yes and this bounces me to the "App info" screen.
There doesn't seem to be anything useful I can do with that, and when I click on "back" I'm back where I was on the "Digital Key" screen which is still telling me the bluetooth is disconnected. It certainly seems as if it ought to work, it's getting me part of the way, but I don't see how to progress.