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/diagnostics/diagnostic.cpp

@@ -10,6 +10,9 @@
 namespace Carbon {
 
 auto DiagnosticLoc::FormatLocation(llvm::raw_ostream& out) const -> void {
+  if (filename.empty()) {
+    return;
+  }
   out << filename;
   if (line_number > 0) {
     out << ":" << line_number;
@@ -17,6 +20,7 @@ auto DiagnosticLoc::FormatLocation(llvm::raw_ostream& out) const -> void {
       out << ":" << column_number;
     }
   }
+  out << ": ";
 }
 
 auto DiagnosticLoc::FormatSnippet(llvm::raw_ostream& out, int indent) const