Danny Sullivan from Google said that any site is able to use the SpecialAnnouncement structured data on their web sites, assuming it is used for COVID-19 or related content. I assumed it was just for official medical and health organizations but I guess I was wrong.
Here is where Danny said any site can use it:
Any site may use it.
— Danny Sullivan (@dannysullivan) April 7, 2020
Note: If you use it, it doesn't mean Google will show it in search.
Danny also said this should be live in the search results soon.
Forum discussion at Twitter.