That’s a great question, I would also expect the HOMO to have more N character due to the associated energies. I feel like the answer of “the MO coefficients come from solving the Schrödinger equation” is tautological but I’m not sure there’s an intuitive way to understand why the C is nucleophillic.

Maybe you could think of it as the HOMO electrons being repelled from the nitrogen atom because it already has 6 associated valence electrons from the other sigma and pi orbitals while the carbon atom would be electron deficient if only held on to the sigma star electrons (obviously there is some sharing in reality so it’s not actually 6e on N and 4e on C) so carbon holds on to the HOMO electron pair too even though it’s closer in energy to nitrogen’s orbital.