Well sovereign citizen argument is just plain stupid; "I live on your soil but your laws don't apply to me because I say so."
Here, youtube is claiming something specific (that Invidious violates a TOS agreement which Invidious agreed to) which is verifiably false - Invidious never agreed to the TOS for the API, and doesn't have to, because Invidious doesn't use the API. Invidious works by communicating with YouTube and scraping data from the responses. There's legal precedent that this is legal (although, LinkedIn's ongoing battle with HiQ may overturn that precedent, but it hasn't yet). That's one of the reasons that most services like youtube offer an affordable API in the first place - 3rd party tools using web scraping is much more expensive for them.
YouTube could still potentially legally force them to stop by changing the TOS of the service itself, but there could be other implications of that, so we'll see what happens. As FOSS, it's unclear what they would even do, there are hundreds of hosts.
That's what I wonder as well. Probably they'll be satisfied with bringing down the Invidious project website, including their documentation and installation files.