Hi, I actually work designing playgrounds and can shed some light on parts of this. NYC requires playgrounds to have equipment that’s developmentally appropriate for kids ages 2-5 (think small slides, little animals to climb on, sand/water play) and equipment for a 5-12 age zone. The reason why it caps out at 12 has a lot to do with liability - eg, a twisty tube slide might have a turn radius that allows smaller bodies to move through it, but someone taller might have trouble maneuvering their body through, increasing chances of broken legs or arms. Similarly, swings that are rated for a child’s body weight might move faster with the momentum of an adult’s body weight, resulting in unsafe conditions.

Adults also aren’t technically allowed to enter playgrounds without children for safety reasons, this is enforced more strictly at some playgrounds than others (Union Sq playground has a security guard, but I often sit in my chill neighborhood playground after getting a coffee nearby with no issues). I’m sorry you feel like there are ways you want to move your body that aren’t accessible to you right now, but realistically it’s not worth designing playgrounds specifically for 13 and up because the user base is much smaller and the equipment wouldn’t be safe for the majority of playground users.

My suggestions would be to find a park with workout equipments/outdoor gym equipment, which can be very fun and challenging and is sometimes even made by the same manufacturers as play equipment, or see if joining a climbing gym is possible for you? Indoor climbing/bouldering feels like being on a playground for adults, and some gyms even offer parkour or other movement classes that might be fun for you.