Will the definition of "fully vaccinated" change as more people receive booster shots?

I suggest we cross that bridge when we come to it.

No. Too much has happened with all of the “not fully vaccinated” to change definitions now.

Tangential statement: I am scheduled for my booster this Friday.

I predict not.
Fully vaccinated stays what it is now; two Pfizer, two Moderna, two AstraZeneca, one J&J (or Sputniks and what have you).
The booster will be just that, a booster on top of an already fully vaccinated person.
I foresee that from next week year we might get/take an annual shot (one or two, but I think one), which will again mean that one is (fully) vaccinated.

Yes, I think the state-issued, verified credentials basically mean “vaccines are up to date”.

Right now in New York State, the Excelsior pass is issued to anyone who is on record for having full vaccinations per today’s standards. This pass expires every six months, right now it can be renewed with the same original vaccination(s) but I expect there will be updates to the requirements to renew it.

CDC says definition of ‘fully vaccinated’ could change as boosters roll out