Add camera rotation to side while keeping input rotation

Hello! I want to be able to rotate the camera to the side you’re moving to (move to right - change the camera roll slightly).

I actually managed to implement this effect (see here: https://imgur.com/a/A72dxNC) but it works by just interpolating the control rotation which totally breaks when you start moving the camera around in first person.

What would be the best way to make this work, please? Thank you for answers.