The US only requires two covid injections no boosters.
This is what I was told by nurse at the medical.
I suggest you email them to clarify and or talk to the nurse over the phone.
You will need to make sure the covid injection(s) is on your GP summary. You will also require the recommended vaccines from the USA like Pfizer, Moderna, etc. They do not like Astrazeneca as its not approved by CDC.