How to GFCI protect a multiwire branch circuit, half hot

This one got me thinking about how it can possibly be done, i'm new to electrical but pretty handy, this is just a bit more complicated than usual.

I have a dishwasher and garbage disposal on what looks like a 20A dual pole circuit breaker (both are switch together at the panel), and going to the outlet under the sink, the old outlet was half hot with red with white at the top outlet plug(always hot), and black wire nutted to go up to the switch and return back to the bottom plug(switched).

My question is can I go GFCI and still use both circuits? I heard I can use 2 separate single outlets and feed power from the other, but that puts both devices on the same circuit and I don't think NEC allows that?

And if the power source is coming in from under the sink at the outlet, does GFCI even make sense since the live power is always there anyway, where water could spill?