Re overhead tree limbs: I live in the south central part of Houston (usually called the Rice University area), whose planners lined the streets with trees. Main Street and the major boulevards in the Rice area were uniformly planted with live oaks, now huge trees in the oldest parts. Because live oaks are broad, spreading trees, they have formed "tunnels" no higher than 16 to 17 feet above the streets throughout the area, which is lower than the canopy in your photo. Anyone living in this part of Houston enjoys these canopies, which mitigate the heat and glare of summer. The example of the Rice area has been followed in most Houston residential areas and along broad avenues as the city grew. Trees grow in this part of Texas as vigorously as anywhere in the Deep South.
There are also highway segments in the region where the trees have created overhead canopies.
My point: to go anywhere in Houston, I must first drive for at least a mile underneath overhead tree limbs. My AP1 2015 Model S (which currently has firmware 8.1 17.11.10) has never given an AEB warning or automatically braked for these tree limbs. Nor has TACC ever braked when passing under overhead limbs. Both AEB braking and TACC braking in my car are fully operational, and AEB has prevented at least one collision. Given the design of the AP, TACC and AEB systems, the automatic braking you describe is extremely abnormal. What you need is a calibration adjustment or some other AP repair at the Service Center.