Switch custom error stream output to diagnostic (#4846)

This switches most error printing to use diagnostics instead of direct
stream writes, even when not a specific file diagnostic. I'm allowing
empty filenames for this use-case.

This allows a little more specific testing to validate coverage of
output using the diagnostic coverage test. I'm adding a few tests to
cover things that weren't previously tested.

Separately, this also forces a little more standardization in format...
considering how changes like #4568 show effort being spent to _mirror_
diagnostic style, my thought is now to just use diagnostic code where
possible.

Note this also allows incrementally better testing of the language
server; I'm changing the crash fix from #4847 in favor of diagnostic
testing.

---------

Co-authored-by: Chandler Carruth <chandlerc@gmail.com>

toolchain/lex/tokenized_buffer_benchmark.cpp

@@ -220,8 +220,7 @@ class LexerBenchHelper {
 
   auto DiagnoseErrors() -> std::string {
     RawStringOstream result;
-    StreamDiagnosticConsumer consumer(result,
-                                      /*include_diagnostic_kind=*/false);
+    StreamDiagnosticConsumer consumer(&result);
     auto buffer = Lex::Lex(value_stores_, source_, consumer);
     consumer.Flush();
     CARBON_CHECK(buffer.has_errors(),