If you share a breaker (IE double tap a single breaker, rather than a single tandem breaker), there is no point in the extra GFCI. You gain nothing but work. You should ignore the extra hot in that case. You don't need it to switch the outlet.

If you want two 20 amp circuits out of this, it's a multi-wire branch circuit.

You can't share a neutral between two separately protected GFCI's if you use standard GFCI outlets (IE you can't run each hot + shared neutral to two different circuits with single-outlet GFCI's).

You can do it with a dual pole GFCI breaker instead.

https://diy.stackexchange.com/questions/20364/can-i-share-the-neutral-in-12-3-cable-between-two-gfi-circuits-with-different-cu goes into detail about this.

Dual pole GFCI breakers can be expensive - like 120 bucks.