Hi,
at the beginning - thank you for a very detailed description of this issue. We have also observed in our office that the includes are not properly noticed by VSCode, but all the projects are compiled without error. This problem was not observed in the earlier versions (of VSCode or Husarion extension).
We will investigate this behavior and I think that the next version of extension will be released soon and will work fine 
I hope that improper handling the includes is the only problem for now and your projects work fine. Sorry for inconvenience.
Regards,
Radek