Anyone knows if there are examples of such states, which were discovered in very specific conditions in lab, to be found outside? Does creation/discovery of such states help in explaining any hitherto unexplainable observations?

The precise state of matter studied in this paper I think is unlikely to exist "naturally".

But yes there are states of matter that exist in nature but are just not obvious until you study them carefully in a lab. For example antiferromagnets exist in nature at naturally cold temperatures (see hematite), but unless you’re looking for them, they just look like normal nonmagnetic solids. Thus they were discovered millennia after ferromagnets.

But there are more exotic states that were first discovered in labs and later theorized to exist in nature, but that have not yet been proven. One example of such a theory is that a superconductivity-like state might occur naturally in neuron stars: https://en.wikipedia.org/wiki/Color_superconductivity

I'll assume you meant "neutron stars."

But "neuron stars" is still an intriguing typo.

Computronium

Always wondered about this.

Even magnets and plasma aren’t blatantly obvious until one sees them in action.

In the early da, someone magnetizing a piece of iron must have seemed like utter witchcraft…

"State of matter" isn't exactly a useful description in this particular case, but it's interesting that enzyme catalysis cannot be explained fully by classical chemistry/physics alone.

https://en.wikipedia.org/wiki/Quantum_tunnelling#Biology

It never ceases to amaze me how many different effects exist in the Universe, waiting for us to discover/exploit. I wonder how many features you could comment out and we'd still be able to evolve, v/s how many of these quirks we depend on for even existing?!