/3 cable and double-stuff breakers, Danger danger!
You really, really need to read my treatise on double-stuff breakers.
Every single breaker in this panel is double-stuff, and the problem is you also have multi-wire branch circuits (MWBCs) - notice the red and black wires on many breakers particularly the ones in the lower left.
That slick trick you are doing, getting 2 whole circuits by running a 12/3, that is a MWBC.
Double-stuffs do not work with MWBC, at least not the way you think, because a double-stuff is not a 2-pole breaker. It is a 1-pole breaker with both hots on the same pole. Using them with MWBC you are bound to set your neutral wires on fire. You already have this problem in several places on this panel.
You must use 2-pole breakers for all your MWBCs (the alternative, handle ties, is not feasible with double-stuffs). Those are called quadplex, as discussed in my treatise linked above.
MWBC (12/3) and GFCI
An entire MWBC can be GFCI protected by one device, but it must protect the entire MWBC which means it must be a 2-pole GFCI unit. Generally those come as breakers, but you will not be using GFCI breakers in this panel!
If I had that panel, I would lay a 42 space subpanel right next to it, and abolish all those double-stuffs. MWBCs are considered obsolete because of how they interact with GFCI (not well). However I think they are fine if you have panel spaces to spare for things like 2-pole GFCI breakers, and why shouldn't you? Spaces are cheap.
Unfortunately given the sorry state of that panel, yes, your only practical choice for terminating a MWBC with GFCI is to push out to a 2-gang box and fit 2 GFCI+receptacle units side by side. You will not be using the LOAD terminals at all.
If you do use the LOAD terminals to continue the two protected circuits onward, you cannot mix their neutrals, GFCI cannot accept that. So you will not be extending onward with 12/3 but rather 12/2/2 or two 12/2‘s.