Publish empty diagnostics on close (#4954)

Without this, diagnostics will linger after closing a file.

This refactors towards a pattern of putting outgoing calls as methods on
`Context`. I'm mixed on this, mainly thinking it's an improvement on
using `outgoing` directly (because it shares the name and structure),
might want to move it to a side-class later that is _only_ LSP wrappers.

I could also make inheritance private on OutgoingMessages and these
kinds of methods public there, but I'm hesitant to adopt that approach
versus a type separation.

toolchain/language_server/handle_text_document.cpp

@@ -58,7 +58,11 @@ auto HandleDidCloseTextDocument(
     return;
   }
 
-  if (!context.files().Erase(filename)) {
+  if (context.files().Erase(filename)) {
+    // Clear diagnostics when the document closes. Otherwise, any diagnostics
+    // will linger.
+    context.PublishDiagnostics({.uri = params.textDocument.uri});
+  } else {
     CARBON_DIAGNOSTIC(LanguageServerCloseUnknownFile, Warning,
                       "tried closing unknown file; ignoring request");
     context.file_emitter().Emit(filename, LanguageServerCloseUnknownFile);