Bathroom circuits code
Yes, bathroom lighting and other hardwired loads are always allowed to be on other, non-bathroom circuits, except for these particular ones:

Not Kitchen countertop circuits, since they must be dedicated to that. NEC 210.11(C)(1)
Not the laundry room circuit, since it must be dedicated to that.  NEC 210.11(C)(2)
Not a bathroom receptacle circuit that serves other bathrooms. (NEC 210.11(C)(3) which is what ThreePhaseEel is talking about.)


However, it's allowed if the bathroom recep circuit serves only this bathroom.



So for instance, suppose your existing bathroom recep circuit, the one you want to extend, already serves non-bathroom loads, but it's &quot;grandfathered&quot; because this was setup before Code changed. That's fine; it gets to stay grandfathered; but you can't use it for the new bathroom.  At all.
The rule of grandfathering is you can't make the situation worse.