Shower drain clogs only when full

I have fully snaked my bathtub drain and can get the snake clearly to the large drain stack for my home. When I run the tap, the water drains at first, but then crawls to a standstill. I have crawled under the house and disassembled the p trap and tub drain, and all are completely clear. The p trap drains to a t-junction in a vertical pipe that leads to a larger drain. This drain travels about 2-3 feet to the main 4-5 inch sewer stack, which is vertical and vents to the roof. Tub water clearly drains, but when the tub is full there is a slight and slow bubbling sound and the drain crawls to a trickle. Any ideas on what to do?

Sounds like it has a venting problem.
Does the tub have an overflow?
If so, is it clear?

Does the vertical tee after the p-trap look similar to the picture I posted?
The Top of the tee going up into the wall. That should be a vent for the tub drain

go on the roof, see if you have a bird nest in the vent

old thread, you have a partial blockage in your sewer,
have the sewer snaked out professionally, it will go away

Crawl back under and install an AAV on the side of the drain