Your scene has nothing in it to demonstrate baked lighting. Two flat planes will generally look the same in this setup no matter what you use. At least place some columns.
Light probes are used to approximate lighting for MOVING objects, but the thing is, an object is not going to use a billion probes. It will pick several nearest ones.
HDRP has a new probe system that is far better than the current probe system, only HDRP for now.
HDRP’s probe system can be used to bake lighting for small objects/props with good quality, can handle tougher objects and lighting conditions compared to the legacy probe system.
You can find it in latest 2022.2 beta, but it’s not on by default.