Those are definitely Mulberries, they grow in trees around the park I go to all the time! My hometown had a lot of them as well. They have a stinky shelf life of 2-3 days even with refrigeration which is why they are not sold in stores. Mulberries have a very good chance at dyeing your lips/tongue/fingers purple when you pick them/eat one as they are juicy and pretty soft. They are close to blackberries and raspberries and you can eat them when they are purple or dark red. They have a stem that is hard to get off and be careful when picking them if they look fuzzy because silk worms might be making a home in the cluster. Some tourists think that they are wrapped in spiderwebs though (some might be, but it's mostly silk worms). Birds here eat them like crazy and sprout new saplings all the time. You can tell when they are ready to eat too by looking at the ground as a lot can fall out just due to weather/heavy winds. The juice can dye shoes and clothes easy too.
Where I am from:
Raspberries typically grow on vines that sprout out of the ground with sharp thorns and have a barbed stem. Blackberries can be vine-like too, but usually grow in a bush. Mulberries are usually in tree form. They all look very similar to each other in shape and in early growing stages. Always make sure to wash your berries before eating! You can make them into a mulberry cobbler or a pie, just make sure to pick the ones that are mostly/totally purple :)
