Olaf, as I said, maybe your library path is wrong?
Installing XData from the installer should not cause that problem, so maybe when you reinstalled, the installer properly updated the library path and now it works.
Yes, Web Core (Pas2JS) should not compile Bcl.Json.Converters, but "Delphi" should. By "Delphi" in quotes I mean the IDE, and that's where code completion comes from. So, for code completion to work in Web Core, the application must be compilable also by DCC32. That's why you should have a correct Win32 library path, so it can find Bcl.Json.Converters. It looks like it was not the case before.