I know Haskell’s LSP years ago just stopped on broken syntax, so the only diagnostic would be the syntax error and you would lose code actions. That was annoying, especially because the LSP was slow.

JetBrains (not an LSP) works up to the syntax error, then recovers and works after. In some cases that are not hard to trigger (e.g. after a closing delimiter), the recovery is wrong and everything after is messed up. But in practice that’s rarely an issue; if I want those later diagnostics and code actions, I fix the delimiters, and the analysis updates quickly.