The quick on the Neutrino Fog: Direct WIMP dark matter detectors are sensitive to nuclear recoils. Neutrinos can also induce nuclear recoils via coherent elastic neutrino-nucleus scattering (CEvNS). There is a point where the dark matter has just the right mass and cross-section such that the kinematics could induce a spectrum that looks just like that from some astrophysical neutrino source CEvNS (and vice versa). This was called the neutrino floor, but more accurately is now called a fog, since it's not a hard limit, but a fluffy bound that makes you slow down progress.
There are different astrophysical neutrino sources that are responsible for different parts of the so-called neutrino fog. The most accessible flux comes from solar boron-8 neutrinos. Those should be detected with the currently-ongoing LZ and XENONnT experiments in the coming year or three. Then there's the neutrino fog from atmospheric neutrinos, that's still a decade or so away.
Directional detection works in principle, since solar neutrinos come from the Sun, but dark matter comes from the direction of the constellation Cygnus. Problem there is the conflict between the need of very significant exposures to get the rate, and simultaneously, a highly instrumented or low-density target to pick up the directionality from the low-energy recoils. I would think of that as challenging-at-best for Solar neutrinos and unrealistic for atmospheric neutrinos.
Sterile neutrinos can increase the neutrino fog, as can other beyond-the-standard-model interactions. This would make the detection come earlier, but to disentangle what goes on would be a fun task for particle physics.
There is one really good way, and that is the multi-target approach. With different target materials, say xenon and argon or germanium, you can break the degeneracy, and disentangle whether the signal in your detectors comes from dark matter or from neutrinos. That underlines why it is so important to have multiple different dark matter experiments at the same time.
