I was thinking of setting up setting up a domain server on Azure and joining from my home network (currently workgroup based).
If you want to deploy your domain server on Azure and join your local PC to it, we should setup a site-to-site VPN.
So my question is whether this is at all practical in this situation? Or will there be too much background traffic on the uplink to make this practical?
Normally, company will create AD DS on local environment, and create another VM on Azure, sync on-prem AD to Azure VM, setup VPN between them, in this way to achieve HA.
In your scenario, we should setup VPN between your local and Azure Vnet, after join the domain, when you login this PC with domain account, it will request to Azure VM, in this time will generate network traffic, but no too much background traffic.
Also we can use Azure AD, join your PC(win10) to Azure AD. More information about Azure AD, please refer to this link.