Does a GFCI-protected bath light/fan unit need separate neutrals?

I hope there is an electrician on this forum who would know the answer to this. I am in the US and must have permits in my area and install per NEC.

This is new construction. Installing a fan/light unit over a shower. I ran 12-3 Romex to them. They are being fed from a load side of a GFCI circuit. They will be sharing the white neutral wire.

Are there any issues with shared neutral when you have a GFI? or must they have separate neutrals?

Any issues with the GFCI not functioning as designed doing it this way?

Any issues with the NEC codes?

Anything else I should know?

see picture of how I have it wired…..