Astra Zeneca - Covidshield

Covishield and Vaxzevria are different brands used for the same vaccine.

Based on the Ministry’s statement, it means that only the following vaccines listed below are recognised as valid proof of vaccination in Italy:

Comirnaty Pfizer-BioNTech by BioNTech Manufacturing GmbH
Spikevax, formerly Moderna by Moderna Biotech Spain, SL
Vaxzvria, formerly AstraZeneca by AstraZeneca Ab
Janssen (Johnson & Johnson) by Janssen – Cilag International NV
For all those planning to travel amid the COVID-19 pandemic, a new tool developed by VisaGuide.World helps you to verify whether the destination you plan to visit recognises as valid proof of vaccination the vaccine you have been immunised with.

Earlier this month, the chief scientist at the World Health Organization (WHO), Soumya Swaminathan, announced that except for recognising the vaccines approved by EMA, 15 European countries have also decided to recognise the AstraZeneca vaccine manufactured by the Serum Institute of India as valid proof of immunity.

Nonetheless, *Italy is not part of this group of countries, despite the fact that the Covishield vaccine has been listed for emergency use by WHO back in February.***

Above from this site--- https://www.schengenvisainfo.com/news/italy-covid-19-vaccines-recognised-for-travel/

I gather there is some variation/version of the AZ vaccine that is NOT acceptable to Italy

Perhaps OP has received this "other" version, thus prompting the question?

I just realised that Covishield are the Indian-made vaccines. It seems like Italy simply requires vaccination with an EMA-approved vaccine, which currently are the four mentioned.

Covishield is not on the list of vaccines under evaluation ( https://www.ema.europa.eu/en/human-regulatory/overview/public-health-threats/coronavirus-disease-covid-19/treatments-vaccines/vaccines-covid-19/covid-19-vaccines-under-evaluation ) which indicates that an approval can be far away. But, on the other hand the vaccine itself is the same as an approved one and it is just a matter of getting EMA-approval for the factory. And I have no idea how long that will take.

I recently read somewhere (I lost the source unfortunately) that the British confirmed many Covidshield batches were actually Vaxzervria which is recognised in Italy.
I received one of the batches originally deemed to be Covidshield and then upon downloading my NHS covid pass yesterday I can see both doses are listed as Vaxzevria. Therefore I'd check yours and if this is the case you'll meet the requirements for entering into Italy without the need to quarantine as things stand today (5th Sept.). This is assuming you're coming from the UK

The UK Government maintains that all the doses received from the Serum Institute of India used in the UK are Vaxzevria, not Covishield. This may not be the case for vaccines administered elsewhere.