I think you’re going to be ok.
On the 2nd line, the info requires “Green Pass” OR negative test...
I think that tourists can get a Green Pass.
Refer to this info on the Italian Gov’t website:
Notizia - Covid-19 - Italy moves ahead with the roll-out of the digital document that makes it easier to access events and facilities in Italy and will facilitate travel in Europe from 1 July. All information can be found on the website www.dgc.gov.it
www.salute.gov.it
I have been to Italy two weeks ago and I have been asked for my vaccination certificate (Pfizer in Australia, in July '21) a few times. Unless I got it wrong during the week I spent there, there is no thing such as an actual pass you get, it refers to the vaccination certificate.
Having said that, I cheated a bit by getting a EU certificate by walking into a pharmac_ in Germany. They looked at our Australian certificate and converted it into a EU one, complete with QR code, stating we had been vaccinated in Germany (which is not true). Right now, our Australian certificates don't have a QR code but most places in Italy scanned that code and got a green tick on their device, whereas Austria and Portugal only want to see the document - actually, in the nearly three weeks I have spent in Portugal, not one venue was interested in seeing any proof of vaccination, I guess that is the result of having 98% of your population vaccinated.
The above is off topic, I know, but on topic I emailed both my state and federal MP again today to ask for an update when more details on borders reopening are expected. In May, I met with our federal MP to discuss the situation at the time, she was only interested in hailing the governments achievements (she is a backbencher, I live on the Central Coast in NSW) and she didn't know anything. So I am not holding out much hope, if there is something of interest to report, I will do this here.