I had a frame where the driveside drop out shorter slot than the other side.
I think its so that the pulley wheels on the gear mech are at a better place relative to where the chain comes off the freewheel
That looks like a Suntour VX mech. Have you tried screwing in the adjuster that makes the mech pivot round the fitting bolt. Then making it go further back.
Also since that might be a 1980s bike. The fork drop outs overlock nut gap might be narrower than modern wheels are. Its 100mm nowadays. was around 90mm before. So if youve fitted a new axle it might be flush with the outside of the drop outs. there supposed to be in a little bit. so the QR ends are gripping on the drop out. not the end of the axle. If its a new axle. you could file a bit off the ends.
If its an old axle. is the bearings and all the locknuts in good order.