Furthermore, we can barely detect neutrinos. Building neutrino detectors is extremely challenging. Usually they are extremely massive and surrounded by lots of rock (even more massive). We'd have to get all that mass to the focal point of the observatory which is extremely far away.
Lastly, the gravitational field inside the sun is much different than outside. In fact, the field is strongest at the surface (or slightly below, as it doesn't have equal density). The further inside you go, the more parts of the sun start pulling you outside, until you reach the center of mass, where the gravitational forces cancel out.
Yes, they are hard to detect, so this is a massive project, not practical right now.
The last point is why there's a caustic. The focal length diverges to infinity as you get to the center; there's a radius where it's at a minimum. This radius will be well within the sun, since the center of the Sun is so much denser than outside the Sun.
The neutrino gravitational focus should be somewhere between the orbits of Uranus and Pluto: https://www.nasa.gov/general/cube-sat-space-flight-test-of-a...