clangd is an LSP. You can use it in any editor with LSP support https://clangd.llvm.org/
Why isn't Cursor using this by default then?
I don't think MSVC provides an LSP, so the VSC C++ extension uses proprietary Intellisense features instead. LLVM provides their own extension to use the clangd LSP: https://marketplace.visualstudio.com/items?itemName=llvm-vs-...
In short: Corporate politics and the Cursor team taking the path of least resistance.