As far as I understand SIM cards, there are just like small crypto chips. You cannon really access the private key on the sim card. The phone just uses the sim

As far as I understand SIM cards, there are just like small crypto chips. You cannon really access the private key on the sim card. The phone just uses the sim card API to sign whatever it needs to sign. So no, the company should not have a reason or way to access your keys, assuming the cards are assigned randomly.