2020 NEC added words to one sentence that completely changed the answer to this question.
210.11(C)(3) Bathroom Branch Circuits. In addition to the number of branch circuits required by other parts of this section, one or more 120-volt, 20-ampere branch circuit shall be provided to supply bathroom(s) receptacle outlet(s) required by 210.52(D) and any countertop and similar work surface receptacle outlets. Such circuits shall have no other outlets.
Then 210.52(D) Bathrooms. In dwelling units, at least one receptacle outlet shall be installed in bathrooms within 900 mm (3 ft) of the outside edge of each basin...
Limitations still exist, such as 210.23(2) Utilization Equipment Fastened in Place. The total rating of utilization equipment fastened in place, other than Luminaires (lighting fixtures), shall not exceed 50 percent of the branch-circuit ampere rating where lighting units, cord-and-plug-connected utilization equipment not fastened in place, or both, are also supplied.
So now NEC says 20A circuits that feed bathroom "countertop and similar work surface" receptacles can only feed those receptacles unless it feeds just one bathroom, then that circuit is allowed feed other equipment in the same bathroom (but subject to 50% of circuit ampacity limitation for fixed in place equipment).
The code is quiet about branch circuit selection requirements for lighting and other receptacles in the bathroom if it isn't on the circuit that feeds the countertop circuit except for the 50% limitation, which likely restricts adding a receptacle to a circuit with your heater and fan.
The GFCI requirement in 210.8 applies to all receptacles in bathrooms.