Not sure if you are referring to the Watch for Tesla app, but that one has worked flawlessly for me. No issues so far... knock on wood.
As for giving a 3rd party access to your Tesla account, I do not know if this applies to all 3rd party apps, but at least for the one I use (Watch for Tesla), I’m fairly concern it has been confirmed that you are not really giving them access to your account, but rather a security token which is used to authenticate your identify and thus allow your AppleWatch to communicate with and access the vehicle. In other words, the 3rd party who owns this app does not really see or has access to your account.