I haven't found "Microsoft .NET Framework 4 Client Profile", only had "Microsoft .NET Framework 4", tried to fix that and got internal error of other kind. But after I get standalone installer of .Net version 4.8 instead of 4.7.2 I had earlier, it had worked well, and Microsoft Update passed as well after the change; so the case I solved, I guess. Still don't know what could have caused such strange behavior, but it's working now, so that's good. Thanks for the advice! :)