If they (the banks) comply with this, it is because they WANT to comply. The President has no authority over banks or any other business. They could take him (Biden) to court if he uses the government to coerce them in breaking the law.
They may not want to (though I think they very much want to), it’s that if they don’t, Joe will sic his DOJ/FBI/Regulators on them. Just easier to give Joe what he wants.