I seem to remember reading that previous year’s vaccines can protect to a certain degree in future years for people who got them.
I don’t have any special insight into the dynamic you address, but I did find this article that seemed to be headed in the right direction to provide good information to you on the subject.
I did not read all of it. I try to caution folks when it comes to medicine, it’s best to get as many opinions as possible, so don’t think this is the final word on it.