Where is the work done of adiabatically expanding universe going into?

Well, there are a few ways to answer this question.

Suppose you draw an imaginary (comoving) box around some region of spacetime. The volume of this box expands over time, so you can think of the contents of this box as doing work on the rest of the universe, outside of the box.

Now, you might say this isn't satisfying if we want to consider the universe as a whole. In that case, you can think of the energy as all going into gravitational potential energy. This is a perfectly good picture in the Newtonian limit.

However, it turns out that in general relativity, it's very hard to make the notation of "gravitational potential energy" precise. For example, you can't talk about the gravitational potential energy density at a point, because you can always go into a freely falling frame there, where the observed gravitational field is zero. For this reason, relativity textbooks generally say that the gravitational potential energy is not defined at all; instead energy (defined as not including this extra ill-defined piece) simply isn't conserved in general relativity. The energy doesn't "go" anywhere, it just vanishes.

If you think this is unacceptable, remember that the only reason we elevated conservation of energy to an important principle in the 19th century was that it was observed to work in everyday situations. We never tested it in exotic situations like those with curved spacetime, so there's no reason to expect the principle to continue to hold up. At a deeper level, Noether's theorem tells us that energy conservation is related to time translation invariance, and we don't have that in an expanding universe.