[clangd] Bump timeouts for LSPServerTests

We seem to be hitting limits in some windows build bots, see
https://github.com/clangd/clangd/issues/1712#issuecomment-1686478931.

So bumping the timeouts to 60 seconds and completely dropping them for sync
requests. As mentioned in the comment above, this should improve things,
considering even the tests that don't touch any complicated scheduler is
failing.

Differential Revision: https://reviews.llvm.org/D158426