Please, help me to understand why my raytracing camera rotates in wrong directions?
The problem is that instead of a camera-to-world matrix, a world-to-camera matrix is being made by glm::lookAtRH. 

This is because GLM is a math library made for OpenGL. In OpenGL, you do not move the 'camera' as there is no camera in OpenGL. You move the whole world the other way around, so that it lines up in the frustum. The lookAtRH method returns a matrix that moves the whole world in a way that it seems like you have the camera there.

Inversing the matrix is a fine way to get the proper camera-to-world matrix.

Scrathapixel does have an article regarding making your own lookAt function. One thing to note about this article is that they use a row-major notation. It might be that you need to switch it up and use a column-major notation (just swap the x index with the y index).

Placing a Camera: the LookAt Function | Scratchapixel