Moultrie makes a micro camera, which is 1/2 of a normal camera size. It says that the batteries last a year. Sportsman's Warehouse sells this in a 2-pack. I got them for $100 because Sportsman's accidentally stuck the 2-pack on a $89 hook and locked it in place, they are originally around $150. I recommend getting a Python lock but cutting the hole in the plastic latch so you can unlatch the cover without having to unlock it from the tree.

https://www.moultriefeeders.com/moultrie-micro-42i-kit

There's also the Shadow Micro Cam by Widgame Innovations, but I couldn't find it on their website.

https://www.amazon.com/Wildgame-Innovations-Megapixel-Infrared-Trubark/dp/B07V7281FT