You might look at cars and presume all cars are gasoline powered. No, "gasoline power" does not define cars and there are other options. Similarly, you might look at GFCIs and presume all GFCIs are "GFCI + receptacle combo devices". GFCIs come in many forms - GFCI+receptacle, GFCI+breaker, GFCI+switch, GFCI as switch, and GFCI only. They're even built into EV "chargers"! All of them provide the "downline protection" feature you just learned about.
On the vast majority of GFCIs, they use a splice feature called "Screw-and-clamp". This allows each screw to screw down and clamp up to 2 wires each. So on your setup, you can add an additional pair of wires to either the LINE side screws (if you do not want downline protection) or the LOAD side screws (if you do want downline protection).
Never put a GFCI in the downline protected area of another GFCI - resetting it after a trip will be very difficult and confusing.
Marking downline outlets is mandatory. You'll thank me later when the receptacle goes dead for no apparent reason and you find you can fix it easily instead of hiring a pro. You can use the ugly "GFCI Protected" stickers provided, or any other marking method which is not handwritten. I like P-touch or Brother labelmakers on a white cover plate.
Also, let's talk about a Code issue. Code requires that circuits which serve bathroom receptacles in the workspace area (i.e. bathroom counter etc. where one might plug in a hair dryer) -- circuits which serve those must not serve anything else. To be more specific, for a circuit which serves bathroom workspace areas, either:
- it serves ONLY bathroom workspace area receptacles in any number of bathrooms -or-
- It serves ONLY receptacles and lighting loads in THIS bathroom.
I wasn't clear where you were extending this circuit to, but if it's outside the bathroom, no go.