It must be a matter of configuration. At work, I use buffer re-fontification as an indicator that clangd correctly processed the C++ source file I just opened. That's with an Emacs built from source ~half a year ago + LSP mode.
Oh, interesting, it does appear lsp-mode now does "semantic highlighting" if the server supports it. I switched to eglot a while back (before it was added), which doesn't.
I don't think I'd want that. Syntax highlighting and indentation are things I want instant feedback from.
That affects the answer to the question. I assume you'd need to persuade lsp-mode not to do this and leave it to tree-sitter, but I don't know how to do that.