Medicare does cover the RSV vaccine if his physician recommends it. I know that there has been a lot of misinformation about RSV and other vaccines the past few years. Part D covers immunizations including RSV, Flu, Pneumonia, Shingles, Covid, Tetanus, and whooping cough. I got mine at a pharmacy (not even the one where we fill our prescriptions) and they submitted it right to Medicare. There was no charge for administering it either. Some friends were told at their clinic that they would be charged an "injection fee" if the nurse did it - they went down the street to Walgreens and got it free from the pharmacist.
Here is the word directly from Medicare.gov:
https://www.medicare.gov/coverage/respiratory-syncytial-virus-rsv-shot#
Sue

If a dr puts in the order to where you wil get that RSV vaccine it is covered
I learned the hard way
My dr put in the order directly to Walgreens
Hope this helps