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/driver/driver_test.cpp

@@ -225,10 +225,5 @@ TEST_F(DriverTest, FileOutput) {
   EXPECT_THAT(ReadFile("test.s"), ContainsRegex("Main:"));
 }
 
-TEST_F(DriverTest, LanguageServerNoStdin) {
-  EXPECT_FALSE(driver_.RunCommand({"language-server"}).success);
-  EXPECT_THAT(test_error_stream_.TakeStr(), HasSubstr("requires input_stream"));
-}
-
 }  // namespace
 }  // namespace Carbon