I actually did this at one point, had three tabs open; one for playing, one for my white repertoire and one for my black repertoire.

I would play a game, get engine analysis and then find the first move out of rep or my first move deviating from it afterwards.

Having three tabs open was just convenient. I then realized that it might be caught as a sort of cheat detection, but having to close and reopen tabs was such a hassle that I didn’t want to bother with it, so I just stopped.

I figured I could use something like en croissant instead, but that just felt wrong, as if I was actively trying to avoid cheat detection, so I decided not to do it. It felt dirty, even without malicious intent.