Pasta alla genovese is one such dish, it resembles modern ragu https://en.wikipedia.org/wiki/Genovese_sauce

That being said I think the ubiquitousness of tomato sauce even in modern Italian cuisine is overestimated.

Onions, carrots, and celery, there you have it. I was trying to find out what renaissance celebrity chef Bartolomeo Scappi typically did for sauce, but I'm not sure. I think mostly meat broth. This tortellini here has a sort of Christmas spices stuffing with nutmeg, cloves, cinnamon, and raisins ... and marjoram and mint and rosewater and saffron ... and sugar and parmesan on top. In meat broth.

https://www.theeternaltable.com/historical-recipes/tortellin...

> Onions, carrots, and celery

This is also a major base of French cuisine and called Mirepoix.

https://en.wikipedia.org/wiki/Mirepoix?wprov=sfti1