Looking things up on Google without being transparent to the interviewer was always cheating the interview.

Its not about transparency, it about what the interviewer assumes about you, first hand. Just like you assuming that whoever is looking up things must be doing it in secret, with the intention of cheating.

It depends - I'm conducting interviews now and I'm totally ok with people screen sharing and showing me their internet searches and AI prompts as part of the interview. Part of the skills I'm hiring for is "can you find the docs/information you need to solve this", so knowing how to use whatever tools you prefer in order to do that is important.

This is actually a great idea, thanks!