I haven't been able to find info of the purpose of the toolstamp. What exactly does it represent, and why does it vary even with identical discs?

It identifies which stamper was used to make the disc. A single glass master is used to make several different stampers which are then used to make the actual discs.

Mastering codes are present on the glass master and get copied over to all the stampers, but the toolstamp and mould text are added later in the process, so they can be different between discs from the same master. (At least that's my understanding.)