Regular expressions are Regular Languages, thus equivalent to deterministic finite state automata. These languages have very interesting properties due to their regularity (eg. pumping lemma), and they are a very small strict subset of Context-Free languages, which are also a strict subset of Turing-Complete languages. If you add recursion and backtracking to RegExps you easily go outside the Regular Languages class, and you probably end up in the TC class. Now you are dealing with an undecidable machine which is also very hard to define and reason about (and you also have two more problems). What's the point of calling it regular?
Your average coding bootcamp kid cracking away in node and invoking the builtin regex engine has no idea what any of those words mean.
To those programmers the words "regular expression" have become completely separated from their original etymology in lexical analysis. To them a regex means "input to a regex engine", and thus the term "use a regular expression" means "use a regex engine". It could be "use a froofroo boingo", for all the meaning the words hold. "Regular expression" just became the vernacular due to its origination in lexical analysis.
Wow, I have no idea what regexps mean? I can write a book about regexps, and if you really want to learn what regexps are, let me know, we can scedule a session.
Anyway, real REGUALR expressions belong to the regular languages class, thus equivalent to DFAs. Given a regexp, you can construct a DFA in O(2^n), where n is the number of operators in the regexp. Now this DFA will have a Linear time complexity match. If you extend regular expressions with backreferences, you can't build DFAs anymore, and you also lose the fundamental property of regularity: the pumping lemma for regular languages. Furthermore, the languages you can build with this extension go even outside the context-free class. Not only that: you are also dealing with an NP-complete matching.
Again, why do you still call them regular?
