I see you have new tires there citizen. Your papers please.

It was poorly worded. TPMS sensors are rarely replaced. I think they have a 10 year/150k mile lifetime.

I have a separate set of Winter wheels which obviously come with their own pressure sensors - so my licence plate/tyre sensor ID pairing will change at least twice a year(I also got a flat once and put a single winter wheel on - what happens then? surely you will get 2 different IDs for one car?).

That's a fair expectation and can be filtered out: you can roughly expect 1 plate to match multiple set of tires. When the same set of tires (or 3 or them) get matched to a different license plate, that can be flagged as suspicious.

New tires won't have been seen on a previous license plate.

Pressure sensors connect to tires to do their job but usually stay with wheels. While not common it's certainly both possible and legal (and sometimes happens) to switch wheels to a different car.

It's fairly common (at least in Europe) for people to have two sets of wheels, on with summer tires and one with winter tires.

Certainly, but keep in mind no one suggested it was either impossible or illegal.

The suggestion above is to merely take note, as it is unusual.

Or legally swapping plates (e.g., personalized plates follow owners to new vehicles, requiring new plates for the vehicle, among other circumstances.)

Or, I suppose, legally swapping wheels, or just pressure sensors.

You don't change plates in the US? Over here(Poland) you get new plates every time the car is sold.