dont know about car services.
but Uber will take you there.... different classes of service available at GRU (UberX, Black etc)... use Uber webpage for an estimate.... likely cheaper option... everyone here uses Uber... free wifi at GRU to summon Uber car.... not all drivers will want to go to Campinas, but one will accept the ride...
or use the taxi monopoly at GRU; called Guarucoop... it is a pre-set price; you pay with credit card at airport booth and you are done; no money due to driver.... it should be about 500 reais one way.
[in case you do not have plane tkt yet... Azul flies nonstop from Fort Lauderdale to VCP airport in Campinas - currently not daily, I think 2x/week]
There is a bus service direct from GRU to Campinas. I believe it is the Lirabus company. The trip takes about two and a half hours, it is direct with no intermediate stops. Or take the Airport Express train to Luz, then Line 1 Underground to Tietê Station for a more frequent service to Campinas (Santa Cruz company is best)
The last time I took this route I took the bus to Campinas . It takes you to the main bus station in Campinas in just over two hours , then you can take a taxi from the main station to your final destination . However , I have returned to GRU to Campinas by UBER and cost me circa 300 Relias . That was in 2019 almost two years ago and thus factor this in your overall calculations . Either sector of the journey were comfortable and I was travelling solo with hand luggage only .