I fly on United, in their "Polaris" business class somewhat often (will be flying to Europe that way in September). United isn't my favorite airline either, but I think it's actually pretty good for a US airline (and their Polaris business class is perfectly nice, nothing to scoff at).
IME, I think most of the time, United cabin crews are generally going to want you to use the lav in your cabin. There will be times when they don't really care one way or another (eg late at night when most passengers are sleeping or trying to). There will also be times when they would actually prefer those seated in the forward sections of Economy or PE to just head up to use the lav in Business Class - while they are serving, and passengers trying to get past them are just in their way.
In your case I suspect it's going to be a YMMV situation - probably no guarantees, nothing in writing, you'll need to "read the room", and just give it a try when it seems OK, being prepared to make a 180 if you get much pushback. Just be polite and fairly discreet, they're not going to open a door and throw you out (no trans-Pacific flights operated by 737 MAX 9s...).
Enjoy your trip.