I recently had the same error message "VPN domain's tap device is down" following a Windows 10 update, after using Hamachi for years. Tried uninstalling and reinstalling Hamachi, problem persisted. Googled lots of Windows stuff, got very confused.
Read your post.
I found two versions of Logmein virtual ethernet adapter drivers in Device Manager, removed them both (with Hamachi still trying to run), then uninstalled Hamachi, then reinstalled, and problem went away. No idea why....
Many thanks.