Yes, it is - the interface is the same but in different colours. Similar to how the apps for all three are the same. Also, due to the historical legal structure of both Bank of Scotland and Halifax being part of the HBOS subsidiary of Lloyds, if you have accounts with both they show in each other’s apps and online banking automatically which is sometimes useful.
As you say, MBNA is also the same (although I don’t have personal experience of them, as I don’t hold one of their cards). Birmingham Midshires is another brand of the group and seems to use a different, more dated, online interface but the basic login process, etc, is the same.
There is no “send money via link” feature, but it may be possible to use something like PayPal or Paym for this instead?
Sorry to hear about this, but it does sound like another point in favour of using credit cards for all everyday spending. That way, you hopefully get any fraudulent transactions sorted before you have to pay off the statement, and therefore don’t lose out. Also, I really don’t like to expose my sort code and account number unnecessarily - and most debit cards still have these details printed on them.