Ciao
I agree that there is no need for you to obtain a second Ph.D, especially if the research topic is similar to what you have already done.
Focus on what you want and work backwards from there.
So you want a post doc/ fellowship position in Italy (or abroad)?
Well...
Can you ask your supervisor for contacts for a future research post? Sometimes lecturers still have leftover funds from a grant (or departmental funds) to fund research. Perhaps your supervisor knows someone who is interested in employing a postdoc. Have you tried applying for grants? Firstly to fund your own research and secondly to make yourself more employable (its a very useful skill). Have you had people contact you from your social media account or website?
Ask different professors in your department for opportunities.
Don't sit and look for answers on a forum. Be proactive and do something about it.
People with successful grant applications stand out from the crowd. Academic research is a competitive market. A candidate with a Ph.D and his/her own funds is an attractive prospect for University departments. Ask your supervisor to look at one of her/his grant applications. As I said, grant application is a skill and you need to apply to several before your successful.
Hope this helps to let you reflect on your situation and what you need to do in the future.