I'm not sure I can think of any example of Genua being portrayed as Italy beyond Bengo Macarena being fond of pasta. (In terms of characterisation, it could be argued that he's a parody of Mediterranean footballers, but he could just as easily be a parody of South American footballers - the name made me think of Maradona - and it's not like any Discworld country has ever been a parody of a single Roundworld location.)
In Maskerade the Italian-ish country is Brindisia.
I'm not sure I can think of any example of Genua being portrayed as Italy beyond Bengo Macarena being fond of pasta. (In terms of characterisation, it could be argued that he's a parody of Mediterranean footballers, but he could just as easily be a parody of South American footballers - the name made me think of Maradona - and it's not like any Discworld country has ever been a parody of a single Roundworld location.)
In Maskerade the Italian-ish country is Brindisia.