What is steric inhibition of resonance

Is the steric inhibition of the resonance or the steric inhibition of the protonation dominant in o-toluidine?

The reason for the reduced basicity is essentially the ortho effect described here: Ortho effect in substituted aromatic acids and bases.

Your question, on the other hand, asks for an apparent contradiction, but I believe there is a little misunderstanding on your part.

We see that because of the bulky methyl present on o-toluidine, the resonance is inhibited, increasing the availability of the single pair of nitrogen.

I don't see how the resonance could be inhibited as this essentially causes the nitrogen orbital of the single pair to rotate significantly to an in-plane arrangement; the methyl group is just not big enough to do this, and if so the If so, the lonely couple would rather turn to the shielded side, which further reduces the acidity.

The highest occupied molecular orbitals (HOMO) of the molecules show this pretty well as they are very, very similar.

At the theoretical level of DF-B97D3 / def2-SVP, the RMSD of the core structure (without hydrogen and methyl group) is negligible with only 0.03 Å.

From this I would conclude that there is no steric resonance inhibition.

On the other hand, the steric inhibition of protonation is given in 2-methylaniline, where it is obviously absent in aniline.
In addition, there is a stabilizing non-covalent interaction between the methyl and amine groups that can be analyzed and displayed with NCIPLOT: the green spot is weakly attractive, red is strongly repulsive, blue would indicate strongly attractive interactions.

TL; DR: The dominant effect is the steric proton inhibition, since the steric resonance inhibition is negligible (if at all possible).