For smaller research groups I expect you’d need to contact researchers and ask for their raw data. Unless you’re an expert in the field expert, they may not be willing to provide.

If you are an expert they probably know of you already and would be happy to collaborate on whatever further research is done using their acquired data. (This happens between experimentalists and theorists all the time).

Some larger collaborations may provide their raw data broadly. Eg, I believe all Hubble Space Telescope data becomes publicly available (the PI’s get some limited time exclusive use to their run data, so they don’t get scooped, but it’s made public later.). Other setups like CERN and FermiLab may do similarly. In these cases it’s up to you to dig deep into the instrument manuals and do your own calibrations and adjustments.

Regarding matching experiment to theory, that’s basically done by experimental research groups directly, in their own publications, probably widely available in the Arxiv.