Okaydoke, the Ministero Della Cultura has finally posted something on their website since I looked this AM so here it is from the horse's mouth. It is in Italian but running the text through google translate:
https://cultura.gov.it/domenicalmuseo
Free Sundays are back in state museums every first Sunday of the
month, free admission to all state museums, archaeological parks and
places of culture.Info and methods of access on the websites of the individual
institutes.Following the adoption of the Decree-Law of 24 March 2022, no. 24,
which sanctioned the cessation of the state of emergency for the
COVID-19 epidemic, free Sundays return to places of culture. Starting
from Sunday 3 April, every first Sunday of the month, the state
museums, archaeological parks and places of culture will guarantee
free access to all visitors who will thus be able to return to benefit
from a unique initiative to promote knowledge of cultural heritage
Italian.Even visits on free Sundays, such as those that will take place during
ordinary visiting days, must take place in full compliance with the
new security measures provided for by the aforementioned Decree. From
1 April 2022 to access monuments, museums, galleries, parks,
monumental gardens of the State, the possession of the reinforced
green pass or the basic one will no longer be required, while the use
of surgical masks will remain.Some locations can be visited by reservation only. The Ministry of
Culture recommends that you consult the detailed sheets before
planning your visit.
Following this text is a list of applicable museums, archeological and cultural sites grouped by region, and live-linked to their respective Ministry of Culture info pages. Those are in Italian but contain links to the individual email addresses and websites for each attraction, if they have them. Very helpful, that!
I'm giving this an "Uh-oh" as I don't know how this will work for visitors who have already purchased tickets/tours. Generally, tours are not allowed on Free Sundays, and it's unsure if people who've already purchased tickets will be given priority, refunds or what-have-you. Also, Free Sundays, aside from Borghese (which is sticking with mandatory, timed-entry reservations for free days but just for a small reservation fee) have been historically been the day you do NOT want to go near the most-visited of Italy's participating sites as they're completely mobbed and queues are very long.
This is very recent news so the museums are probably scrambling to figure out how they'll individually handle the details. I glanced at the ticketing sites for some of the biggies and noticed that they weren't selling any tickets for Sunday, April 3. As the Ministry recommended, anyone having tickets for/planning to visit the bigger museums/archeological sites on any upcoming first Sundays of a month should reference the individual websites for those venues for additional info. I'm guessing that anyone with tours booked for those Sundays might expect some communication from the booking source as well.