I have a house in Sicily which I inherited from

There are others better qualified in this community to give you an answer but there are grants available for major works. You don't have to be resident.  There is a deadline for submission and completion. A chap on YouTube called Not Useless Yet has done a quick summary that will give you an idea. 

As a non resident and non taxpayer you wont be eligible for most of the incentives, which are deductions on tax payable over the next 5/10 years.  BUt you should be eligible for reductions in IVA, green energy incentives etc - and the 110% superbonus, but that depends on many things, and it could well be too late to think about that.   Other bonuses you can get as a 'sconto in fattura' so you just pay less at the till, and the seller gets the bonus - which is true for solar panels, some white goods,  etc.    Until you know exactly what needs to be done, its difficult to say.   It does also mean that all work must be paid for in a certain way (by bank transfer) and with a pretty involved paper trail which your geometra will sort out. 

I am also looking into this issue for 1 euro houses. The full list of Italian cities for 2023 is here. And I can say that I also have a misunderstanding of this issue. On the one hand, it is clear that there are costs for processing the transaction and for a notary and other fees in the region of 5,000 euros, but on the other hand, there are such things in Italy as various bonuses for repairs and insulation, and even for improving earthquake resistance that can make a house and repair cheaper. How does it work for visitors to Italy .. so much information and everyone says different things (