I'm sure this is clever, but wow, it's awfully dense. If you were writing code for production, it would need a lot of comments!
But I think you were not writing for production.

Im gonna take this

What does this do? Please some comment or description.

Good, but the same regExp is evaluated twice on a given string which is inefficient for very long inputs.
That can be optimized.

Impressive. very nice.

Really clever !

for these regex ones I'm not quite sure I understand how they verify that one pair doesn't close before an inner pair is closed?

Nice solution, but Imho I've made a bit better one.
You run regex twice for each iteration.
Checkout mine solution. It uses only onre regex per cycle and compares string length change.

This is where a lot of coders fail. Trying to optimize stuff that doesn't really need to be optimized. Unless if the specs tell you about repeatedly processing enormous strings with limited resources, parsing strings with a stack or regexp is going to be essentially the same.

If both solutions meet specs, then both are efficient. Of course, you should plan a little flexibility into your solution based on implied specs, but there were no implications in the short description. Very straightforward problem with a very straightforward solution.

The nice solution!
I'd suggest to create the regexp once as a const.