I can't see a reason former first world powers
wouldn't have some operational aircraft post-TDM. In the US there are literally thousands of private small aircraft sitting on the tarmac or in hangars of hundreds of municipal airports. These are besides the military aircraft not destroyed in combat or nuclear strikes. Even the magic EMPs of T2K aren't going to destroy every single electronic component in every one of these aircraft.
Aircraft rendered completely unusable from the EMPs will be canabalized to provide spares/repairs for other aircraft. Small aircraft would be some of the highest priority equipment any power bloc (MilGov, CivGov, etc) would want to control. I'd even say aircraft would be higher priority than heavy armor, tanks are well and good but aerial recon gives a huge advantage to even a light infantry force.
Avgas for planes wouldn't be any more of a problem than fuel normally is in T2K, after all somehow Diesel engines can run on alcohol.
Avgas and gasoline can be made from syngas with some processing, synthetic avgas has actually been a thing for years in civil aviation, the FAA allows up to (IIRC) 50% natural/synthetic avgas blends. Synthetic fuel was heavily used by Germany in WWII and chemical plants that made it were primary targets for allied bombing. So avgas would be something larger powers could end up making in bulk. Not commercial aviation is practical bulk production but enough to perform aerial recon and high value transport.
At the local cantonment level I think kites and balloons would definitely be used if not ultralight planes or paramotors in some places. Kites and balloons could be used for aerial photography, weather stations, or to loft radio repeaters to extend UHF/VHF comms.
I don't think what air power anyone can field would be used in front line combat very often though. With no armor or defensive systems repurposed civilian aircraft wouldn't want to get anywhere near enemy ground forces. They'd prefer nice safe high altitude missions.