Change camera FOV to keep 3d scene same size on screen, independently from resolution

Much like the title. I have a Perspective camera in a 3D scene, and with that I need to keep the visuals always at the same physical size on screen, regardless if I change the resolution and aspect ratio of the game window during play. This because there is a particular billboard object in the scene with pixel art graphics; I can't scale the object for gameplay reasons, so I'd need to scale the FOV to keep that object at the physical size I need.

Easy to do with UI (constant pixel size) but what about 3D stuff? I'm pretty sure there is a way to link FOV with screen height and width, but after searching for hours I feel a bit burned out and can't come with a solution.