Now that is a QFT question I can’t personally answer with precision, but the gist I get is that trying to measure virtual particles is like trying to measure water molecules while submerged. Your virtual photon detector will always register virtual photons, coming from every direction. I do know every question about particle interactions has an equivalent question about field dynamics, since the discovery of the two being the same was a historical milestone (but Feynman diagrams are the easier way to keep track of what your integrals mean).

For photons themselves, you can learn things using just the force. We’ve ruled out any significant rest mass for photons that way, because it would show up as electrostatic force penetrating conductive barriers that should (and apparently do) shield it. I guess to know the mass of a Higg’s boson, though, you need to make actual tangible particles and record their decays (in tiny, noisy increments until you narrow it down enough). There’s a lot of different moving parts in the Standard Model so it shouldn’t be too surprising it’s hard to nail down certain parameters exactly with indirect methods.