Ahhh, "extension" meaning not in the POSIX basic definition. Sure. Though I don't know many tools that implement REs in that basic form. They almost all include features outside that definition.

No, extension as in it is not regular. Nothing to do with POSIX. RE2, Go and Rust do not provide backreference support in exchange for predictable performance.

There are plenty of regex engines that are guaranteed O(n) for all regexes they accept. There's re2, go-regex, and rust-regex just to list a few popular ones.

They still use Perl-like syntax, and might still be able to parse non-regular languages, but you don't need to worry about users deliberately crafting regexes to eat up CPU time like PCRE.