Mgkbh The only thing I might add is when HPLIP has been prickly in the past, I go directly through CUPS and id the model/driver online. As for my HP, it works perfectly on Solus Budgie and I installed via HPLIP.
That being said, I've always had issues with HP detection in the past, regardless of distro. Makes me wonder what printer I am going to get once this one dies.