15000 btu on a 3000 watt genny is going to be marginal. It's the start up that is difficult, once it's running, doesn't draw nearly as much.
A couple suggestions. Google hard start capasitor mod and check and see if your ac has one. If not, add one.
Secondly, use your circuit breakers to kill everything but the ac that has a circuit breaker for 110v. Give it a try then and then once it's running, you should be able to power back on.
You don't say but altitude can make a genny not run at peak power so if you've been camping at higher altitude than when it ran before, that might be part of it. Also hotter weather makes the ac work harder. Mine will start up while plugged into the house in the spring but blow a circuit breaker in the summer because it needs more than the 20 amp circuit can provide it.
2015 GMC 2500 Denali Crewcab 4x4
2019 Forest River Wolfpack 23pack15
Hope your travels are safe and the friendships made camping are lasting.