Looks like the COVID-related issues are messing with more than just flights. From the cathedral's website:
https://duomo.firenze.it/en/home
Following a reduction in staff due to the pandemic, today the Duomo is
closed to tourists. At the moment it is not possible to say whether it
will open in the next few days but access for worship is guaranteed.
Staffing issues don't look to currently be affecting the other parts of the complex. Just a guess but as those other parts involve paid ticketing, they've probably shuffled available staff around to keep them open and avoid refunds. Anyway, just a head's up for anyone in Firenze the next few days, and a reminder to frequently check websites for sightseeing attractions 'cuz things can change on a dime!