Alright scrap that - it's working! 🙌 Also did nothing differently than when I tried late last night.

I have a suspicion that this might be due to being an Apple One subscriber but having separate iCloud and App Store accounts - in that case you are billed via the App Store account, but iCloud+ gets added to the iCloud account. I wonder if this is making it look like I don't have iCloud+ as the account I am logged in on is not the billing account which leads to this generic error. Can anyone else who has this exact error confirm whether or not they have a similar setup please?

Well apparently this feature is now out of Beta with the launch of iOS 15 and is available for configuration on standard iCloud.com. AND YET I still cannot add any email addresses after configuring brand new domains.