Unfortunately working with private repositories on Windows seems to be a long standing issue. You’re far from the only one to have experienced this. I could be wrong but as far as I know it hasn’t been resolved. See the following thread for more info:
Seems like the standard workaround is to use https. That is what my company has done to accommodate Windows users. If https isn’t an option then I’m not sure what the best path forward is. There might be a way to get ssh to work on Windows.