When calculating absolute magnitudes of distant objects, do you use the light-travel distance or the comoving distance? I want to calculate the absolute magnitude of GN-z11. Its light-travel distance is 13.4 billion ly (4.1 Gpc), its comoving distance is 32 billion ly (9.8 Gpc), and its apparent magnitude is $25.8$. Calculating its absolute magnitude, we get $M=-76.86$ for light-travel, and $M=-94.09$ for comoving. Which one do I use? I am assuming it is the former. Is this correct, or is there a different formula for this?
Neither. You use the Luminosity Distance.
$$M = m -5\log D_L + 5$$
This assumes bolometric magnitudes. If you are trying to estimate it in some photometric band then you must also calculate and apply a K-correction that will depend upon the intrinsic spectrum of the source.
For $z=11.09$ this cosmology calculator gives a model-dependent luminosity-distance modulus of 50.39 (corresponding to $D_L=1.2\times 10^{11}$ pc).
NB: The distances you quote in the question do not give the absolute magnitudes quoted.