It was open but now seems to be closed as tickets unavailable on various sites.
Any information when it might re-open again. Will be in Rome in October 2022.
The website says this:
https://www.mausoleodiaugusto.it/it/booking/
"Dal 6 giugno il Mausoleo di Augusto chiude temporaneamente per consentire l’avanzamento dei lavori di riqualificazione di piazza Augusto Imperatore.
English: "From 6 June the Mausoleum of Augustus closes temporarily to allow the progress of the redevelopment works of Piazza Augusto Imperatore."
Rome's official tourism site states the same:
http://060608.it/en/cultura-e-svago/beni-culturali/beni-archeologici/mausoleo-di-augusto.html
Both provide visiting hours for October so maybe that's when it's expected to re-open. Maybe they're not pre-selling tickets as they're not sure of the re-opening date.
Timetables
1st October - 14th October from Tuesday to Sunday 9.00-18.30 (last admission 17.30);
October 15 - October 30 from Tuesday to Sunday 9.00-18.15 (last admission 5.15pm);
October 31 - March 26 from Tuesday to Sunday from 9.00 to 16.00 (last admission 15.00);
24 and 31 December (last visit at 12.30)
27 March - 21 April from Tuesday to Sunday 9.00-17.00 (last admission 16.00);
April 22nd - September 30th from Tuesday to Sunday 9.00am-7.00pm (last admission 6.00pm) - closed on May 1st;