alt Hacker NewseBay is hyper aggressive about fingerprinting, they will catch things like it trivially. Browsers leak all sorts of information like what sockets are open on localhost, making yourself look like an actual person is very challenging to someone motivated to detect you.
LLMs don't need browser automation though. Multimodal models with vision input can operate a real computer with "real" user inputs over USB, where the computer itself returns a real, plausible browser fingerprint because it is a real browser being operated by something that behaves humanly.