> if the language has type inference, which all modern languages do
Well, only if your "modern" language is a statically typed language ... And again: Unless your code is correct and complete, you really can not just run "eval" in your source language and obtain type checking out of the box.
However, from what I understand it seems to supply just a parser separate from the Rust compiler (https://github.com/rust-lang/rust-analyzer/tree/master/crate...) trying to keep up with Rust‘s development. So, in principle, it could have been just another treesitter parser plugin, too.
So, again, the LSP framework does not directly provide any magical benefit over a static parsing framework. All the semantic analysis capabilities stem from a good parser.
Rust analyzer also provides compilation errors, lints, and code actions. It would be a lot of unnecessary work to implement and maintain these functionalities five times in five different editors.