according to a new EU law, you can not open, or maintain, a European bank account without proof of residency
no such law/regulation exists. Bank accounts for non-residents are a very common product in at least the bigger commercial banks and it will continue this way, it's just normal business. It might just be that some banks are not willing to deal with foreigners, in particular - in the case of US residents - with FACTA reporting. Or exclude at will like mBank currently states that "mBank does not offer its services to customers in the United Kingdom", for whatever reason, but that is their choice, not a law.