Chainlink V0.8 no longer includes the Oracle.sol class that I used in V0.6 to register the chainlink node. It seems Operator.sol replaced that in V0.7 (which I never used). However, the only implementation of ChainlinkRequestInterface in V0.8 seems to be OperatorInterface.sol.
How to deploy the node operator contract using V0.8 properly?
You'd use Operator.sol in v0.7 and v0.8. You can use the interface to interact with a v0.7 edition of Operator.sol in v0.8