Hi, what would be the best game engines to make a 2d side scrolling shooter and a 3d motorbike racing game on Linux? I would like it to be in c++ if possible, thanks.

Unreal could likely work for you.

Godot aims to be cross platform and unlike Unreal, it seems to be easier to get started

Allegro 5 is alive and kicking, and supports everything necessary for working with DX/OpenGL directly.

I would use Allegro5 for the 2D stuff, and throw in OGRE for the 3D or your favorite collision engine.