Integration services are no longer automatically installed or automatically available, to guests running operating systems older than 10, on hosts running 2016. They have to be installed by powershell or DISM, directly into the guest, not the host. I found DISM to work when powershell didn’t. The appropriate image addition is downloaded here:
and then installed thus, e.g. for Windows 7/2008R2:
DISM /Online /Add-Package /PackagePath:C:\storage\windows6.x-hypervintegrationservices-x64.cab