Does VS Code support more refactoring and code generation now? I last used it heavily over a year ago, and at the time it seemed like anything beyond moving files and renaming things wasn't really doable. Meanwhile, in JetBrains's software I can extract and inline variables and functions, change signatures, split things out into other files, and more. I think I tried a plugin or two which were supposed to handle those things, but they either just didn't work at all or weren't reliable.
Depends on the language LSP. From my experience, it works VERY well for JS, reasonably well for Go and not that well for python. Python allows you to refactor variables if it knows the scope of it but won't work if you use star imports and moving files doesn't work at all
It all depends on the language plugin. rust-analyzer can do a lot of this stuff, I haven't seen much of it for TypeScript (though you tend not to need it as much in more flexible languages), not sure about other languages