I've been noticed by a friend that Sardinia currently requires advanced registration before travelling due COVID-19. The registration page is in Italy, no English, so I'll ask the embassy. But maybe somebody here knows more.
OK, according to Czech embassy in Italy [in Czech], it's needed either to be registered on http://www.regione.sardegna.it/ or since 12th June it's possible to fill this form on the airplane and hand it in to the officers in Sardinia.
The online registration form appears to be: https://sus.regione.sardegna.it/sus/covid19/regimbarco/init (found on http://www.regione.sardegna.it/j/v/2834?s=1&v=9&c=94253&na=1&n=8&c1=289&nodesc=1&ph=1&c1=3).
It also requires to add at least 1 location (address) where traveller is planning to stay (ID appointed there is required).
After registration, the autority will send you an email with a confirmation ID and an additional link to another form (health check and possible covid-19 infections) that is mandatory to file-in 48h before the departure date.
http://www.regione.sardegna.it/xml/getpage.php?cat=65 states that
for more information about this process, it's best to send an email at:
UPDATE: after filling a form I got confirmation with assigned ID and GUID and link to my form where I'm required to fill my health status declaration 48 hours before the boarding date.