Changes to enable the module conversion script

* shorthand -> long for `factory` since the typeformer script doesn't
  know how to handle it.

* Use setter to change `ts.sys` (similar to #35399).

* Fix `loggedIO` with empty namespaces to indicate dependency
  (similar to 50603eda).

* Move `Map` / `Set` stuff from `core.ts` to `corePublic.ts` since the
  types are there.

src/tsserver/webServer.ts

@@ -78,7 +78,7 @@ namespace ts.server {
         };
         // Do this after sys has been set as findArguments is going to work only then
         const sys = server.createWebSystem(webHost, args, () => findArgument("--executingFilePath") || location + "");
-        ts.sys = sys;
+        setSys(sys);
         const localeStr = findArgument("--locale");
         if (localeStr) {
             validateLocaleAndSetLanguage(localeStr, sys);