Maybe you should care about the output match!
You do not define what you mean by gain, but if your "gain" is 20 log s21, then the gain is being calculated with a simulated 50 ohm load. If you have a poor output match to a 50 ohm load, you will have less overall gain. If you have a good output match to a 50 ohm load, you will have more overall gain. It does not matter if at some later time you want to hook this up to a different load. We are talking about the bump in "gain" that you showed in your plot, and we only care right now about the load that the computer software used during the simulation.
If, at -23 dBm input power, the output impedance shifts so that you have a much better match than when you have -30 dBm input power, that could explain the 3 db jump in gain.
This is just a guess, but a 3dB bump in gain is not that much, and could be a large signal impedance effect, especially if you consider a match to some harmonic generated at the higher output power.