It is good that it is not leaking.
And I understand that the trap adapter is glued to the pipe.
My point is that the trap arm that goes into the trap adapter is quite short, basically just the 90-elbow part of the trap arm. You have the slip joint nut/gasket for the trap arm that could be causing stress on the P-trap nut/gasket that was leaking due to that geometry. Had you cut more off the pipe, after you glued the adapter on the shorter pipe you would have a longer trap arm that was part of the trap assembly. That would provide a little more flexibility in the trap assembly joints. Adding a thicker gasket isn't necessarily a bad thing, but again it really shouldn't be required if the assembly is installed properly.