Should I simply delete the printer and reinstall it?
That seems to be a popular troubleshooting method.
Uninstalling the associated software is also a good idea.
Then be sure to get the latest full featured driver / software package that HP has for your printer. Hopefully something that supports Windows 10 for your scanner.
Unfortunately, for me (HP OfficeJet 4500 G510n-z) some of the HP Software features will just not install (Toolbox, Solution Center, etc.) but the printer still prints fine and scans as well, when connected to USB, and the wireless printing function, still works for the other computers on the network.