Congratulations for the productivity !
In the free version, and without coding php: to solve your question, the reply is to use the bulk actions method edit in the posts list… twenty by twenty – it take to you 4 x 200 clicks… it is long but it is an efficient way…
Another method is to add a temporary add-on (php file) to xili-language containing pieces of code and loop to assign the good taxonomy (it_IT) to each of the 4000 – It needs preliminary tests to size the maximum loop steps (100 ? 200 ?) due to the available memory in your server !…
A sql query will be to much complex so this loop uses current wp function to assign taxonomy !