Syntect's grammars are regex based, they're based on ST3's grammars which are an extension of the fundamental model used by Textmate/Atom/VSCode. They're stronger than just regexes though, there's a fancy stack machine with all sorts of features laid on top that allows it to do full parsing of a lot of languages.

The more modern grammars are written with a regex style that makes heavier use of the stack machine and so only uses regexes that can be turned into a DFA. There's ongoing work to use a layer on top of Rust's super-fast DFA-based regex engine to accelerate these grammars https://github.com/trishume/syntect/pull/34.

The problem with using non-regex based grammars is that you have to write them yourself. Syntect is something like 4000 lines of code but the grammars it uses total around 35k lines, and that's just the included ones, not the full ecosystem of online grammars. Basically unless you only want to support a small set of languages, a non-regex-based highlighting library is fairly infeasibly for a single hobbyist.