Hey @dtp5! My suggestion would be to, instead of stubbing the authenticate method, run the tests using an ethers or web3js provider connected to your local dev network (ganache or hardhat network), or a full mock object. See the relay example in the autotask-examples repo: the Autotask is split into the Defender entrypoint (that sets up the DefenderRelayProvider) and the main logic (that uses the provider).
The tests then create a different provider, and call the main function directly:
Alternatively, if you do want to stub out the function that authenticates the Relayer to the API, you need to stub out the DefenderRelayProvider.relayer.relayer.init() async method, which returns a Promise<void>.