I do all my banking online. My bank sends out checks for payments, not me. Recently sent one out to a new payee that never hit the account. Actually received the check back at my address....unable to deliver no such address. I must’ve looked at that thing 10 times and couldn’t figure out why. Laid it aside and a couple of weeks later when I was getting ready to pay some bills picked it up again. I had transposed 2 numbers in the address. lol
If there is a physical bank, I'd drive to it and meet face to face with a representative.
Also, the routing number is different from a mailing address. Banks and the IRS use the routing number to transfer payments electronically. It is a rather long nonsensical number (usually the number at the bottom of your paper check) and it is easy to make a mistake. However, your bank will be able to sort it out for you and you will know if there was ID theft.
Also, it is moot for this transfer, though since the IRS has already given up and will be sending a paper check.
Good luck!