We visited Puglia, including Lecce, last November. We had a rental car until we got to Bari at the end, so weren’t using as much public transportation as it sounds like you’re planning.
I did want to mention the masseria where we had a really outstanding Sunday lunch. Masseria Filippo de Raho is close to Lecce, so I’d imagine that a taxi ride would be relatively easy to manage both in time and cost. I’d say the lunch was Michelin Star worthy, although it’s not a Michelin place. As we didn’t stay there, I can’t offer any experience with their lodging, and while they have some niceties, I don’t believe they have been converted to a total spa resort, unlike so many other masserias nowadays. Their Website lists several Exoeriences they offer, including a cooking class, but again, we were just there for the one wonderful lunch. We did have to push a button on the intercom at the gate to get buzzed in with our car, but once we made our way along the driveway to their building, it felt welcoming and not like an exclusionary resort. Website is https://www.filippoderaho.com/en/