Most LSP server implementations I've seen are just parsing the source or even stop at just tokenizing it. They don't do anything magical inside the source language (unless a language exposes parsing/compiler internals e.g. like Raku's language server does). So I don't think most LSP servers leverage anything from inside the source language's compiler including performing type inference on your code snippets. Also note: If your code snippet is complete because you are just about typing it, this also cannot work in principle. That's exactly why treesitter was invented: To have a robust static parser able to process incomplete or erroneous code.

> 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.