If I change the camera's Projection property to Orthogonal, the deformation doesn't occur.
Godot 3.5.2-rc2 works the same way, so I don't think it's a bug.
I have little experience with 3D in Godot, and don't know if that mouse pan/tilt behavior can be customized other than with the camera. There are people here with much more 3D experience who probably have more insight on this.