Automated testing (there aren't different kinds; to try and draw a distinction misunderstands what it is) doesn't catch bugs, it defines a contract. Code is then written to conform to that contract. Bugs cannot be introduced to be caught as they would violate the contract.

Of course that is not a panacea. What can happen in the real world is not truly understanding what the software needs to do. That can result in the contract not being aligned with what the software actually needs. It is quite reasonable to call the outcome of that "bugs", but tests cannot catch that either. In that case, the tests are where the problem lies!

Most aspects of software are pretty clear cut, though. You can reasonably define a full contract without needing to see it. UX is a particular area where I've struggled to find a way to determine what the software needs before seeing it. There is seemingly no objective measure that can be applied in determining if a UX is going to spark joy in order to encode that in a contract ahead of time. Although, as before, I'm quite interested to learn about how others are solving that problem as leaving it up to "I'll know it when I see it" is a rather horrible approach.