I don’t know the answer to this but I wonder if Senators - who have residences in Washington as well as their home states - get per diems at one or the other. Or both. Just wondering.
Travel for the purpose of commuting to work is not reimbursible. I'd guess Joe Biden does not get reimbursed ~ or maybe he does. Someone should find out.
BTW, Congress has its own rules ~ it's a separate branch of government and no one there needs to follow the Executive Branch travel rules ~ although, in general, whatever Congress does in this regard will look pretty much like what everybody else does.