Are Cal Kit (SOLT) definitions unique by serial number?
It could be either way. 

Some kits are characterized individually, some only by model number.

A high priced Keysight kit is probably characterized individually, but you could check with Keysight to be sure. If it is individually characterized, they should provide new characterization data with the replacement standard.

However, I was told by one cal kit vendor (not Keysight) that even though they charge more for an individually characterized kit, they actually think their EM modelling is more accurate than the equipment and references they use to do the cal kit characterization, so the generic characterization data provided with the lower-cost kits is actually better than the measurement-derived data provided with the individually characterized kits.

So your mileage may vary.