In June I went overland in Mongolia 4500 km: BayanUlgii-Khovd-Uvs-Zavkhan-Arkhangai-Dundgobi-Umungobi-Dondgobi-Tuv-UB. No problem getting any petrol anywhere, though it is expensive. In UB people still say that some petrol stations sometimes do not have fuel, but all the ones I saw had fuel. There is also a plan for Russia to provide more very soon so I think the main part of the crisis is over.
I don't know the situation with diesel but I saw many trucks in the countryside so they must be getting diesel somewhere.