I had COVID recently. It was not fun for about a week, my case was thankfully not too severe and I was prescribed good treatment with Paxlovid (pill that helps treat COVID now).
The good news is now that while the pandemic is still ongoing, doctors at least know how to treat it better, and there are multiple legitimate treatments now for COVID that can help you feel better and curb the symptoms. After I was diagnosed, I was very encouraged with how knowledgeable medical staff and doctors seem to be about COVID now and how to treat it.
Provided Cavill doesn't have a severe reaction to the virus, he should be good to go again soon and production should hopefully resume very soon.
Season 3 sounds like it was pretty deep in production already. But considering that Cavill is one of the central leads, it sounds like they just couldn't move on and do more without him. Especially if they were doing things like the Thanedd ball and coup.
And considering that, provided his case is not too dangerous, it's only going to be a temporary halt.
Also, the halt might be necessary to monitor other cast and crew members who had close contact with Cavill to make sure they don't get sick either. Like they might need to temporarily quarantine too in case they become symptomatic as well.