The most important word in the title is "class". It only does this properly for JS code inside an explicit ES6 class, and, after some cursory testing, doesn't work too well if you bind things to the class at runtime/outside of the main class block.

VS code doesn't autocomplete "this" for "old-school" (function-provided "this" objects and manual prototype inheritance etc.) object-orientish JS; it doesn't compute it properly or at all for re-bound "this" (e.g. apply()/bind()).

Making autocompletion analysis work for non-straightforward non-ES6 OO javascript is a very hard (maybe impossible even without any "eval"ed code, though I'm not sure) thing to do, so this isn't a ding on VS code: any autocompletion is better than none.

That said, if the only way to get good OO-code autocompletion is to reduce the subset of the language/OO models usable to basically "what you could have in Java/C#", it might be a good opportunity to re-evaluate your choice of language. Transpilers for more easily-statically-analyzable languages do exist, after all.