There is very little information on the use of the Key Distribution Service, in relation to gMSA. it just says 'The Microsoft Key Distribution Service (kdssvc.dll) provides the mechanism to securely obtain the latest key or a specific key with a key identifier for an Active Directory account'. But doesn't mention what the key is used for. The root key that is used when the gMSA is created is stored against the gMSA object in the msDS-ManagedPasswordId attribute. The current and previous passwords are also stored in the gMSA object and can be retrieved by the allowed principal, this doesn't require the key to access this information. So there must be an RPC service or something similar that is using the key to access the password when the Windows service tries to start.
I think based on your observations and rereading the note above again, deleting the Key Root will impact any existing gMSA that were created using that root key.
Do you have the option to restore the deleted Key from CN=Master Root Keys,CN=Group Key Distribution Service,CN=Services,CN=Configuration,DC=<yourdomain>. If not, then you might need to recreate and reinstall all your gMSA accounts based on the deleted root key.