[model-gateway] reorganize integration tests into logical subdirectories (#16451)

sgl-model-gateway/tests/api/mod.rs

@@ -0,0 +1,7 @@
+//! API endpoint integration tests
+
+mod api_endpoints_test;
+mod parser_endpoints_test;
+mod request_formats_test;
+mod responses_api_test;
+mod streaming_tests;