I am looking at purchasing an apartment in Bari that

If the real estate agency, or the seller, are unable or unwilling, offer this service, for free - And maybe even in this case, because it could be an unrealistic quotation, aimed at selling - It is necessary for you , identify and pay a trusted technician to make this calculation for you in line with your restoration needs

If you are interested in buying the property to renovate - you should approach the process exactly as you would in your own country.

Of course it is much more complicated by not living in Italy and probably with linguistic barriers plus Covid thrown in the mix. Nevertheless - do as you would in your country i.e. find a Geometra or Architect who is independent from the seller and agent  - who will give you a market price for the renovation project  - initially you can ask for a simple ballpark price with basic description of what you want to do. This service will be inexpensive and be a business introduction for the  Geometra or Architect, so they will do it for very little money – if you need to work with an English speaking Geometra or Architect – so be it. It will be possible to find one on this or other forums. However it is important to find one without asking the estate agent to provide you as there could be a risk of the Geometra or Architect working in the Agents/Sellers’s interests.