Hi Jules,
The company listed below is who I used to rent an ebike to go out in the countryside by myself in the afternoon for the enjoyment & also to photograph some trulli ruins, etc. They also have private tours, segway tours, tuk tuk tours, etc.
I was walking early the next morning in town, and the owner called out to me and was very friendly, asking if I had a good time in Alberobello, etc. He treated me like an old friend.
https://www.allwayspuglia.it/en
Are you planning to also go to nearby Locorotondo? Some of their private tours include both cities, and I would recommend that option. They are very close to each other, yet very different styles. I know it’s common on the forum to hear recommendations to avoid Alberobello or only stop for an hour. But, I stayed overnight in both of these small cities and will be staying in both of them again next May.
There’s no shortage of souvenir shops in Alberobello! A lot of them are things you probably don’t want, but I did see a couple of artisan shops. They’re mostly in one section of the town; they will be easy to find.