I realize that I may be late in commenting but I have helped a few people learn to tread who believed they couldn’t float or tread. The real help will be in working your lung capacity. While there are some who’s lung capacity is below norm, most people don’t realize they are not using their total lung capacity. I usually start with getting daily practice of doing the 3 deep breaths and holding while floating (or sinking to shallow end) for as long as possible. (practice the slow exhale so you don’t screw that up with bad habits) Try to relax, close your eyes and think of something else while someone else times you.
Then work on deep DEEP breathing all the time to expand your lungs and diaphragm abilities.
When you tread, half float and half tread. Hold your breath for 30 secs while slowly moving arms forward and back with palms down and providing lift like you did as a kid and put your hand out the window. Legs in long tip toe’d straight leg strides (like you have fins on). Have your arms and legs providing lift in an offset pattern where each is providing max lift when the other is a min lift.
The drown proofing is something I learned back in the 80’s and is great. Understanding the physics of your body and that you are mostly water which is neutral in water makes relaxing easier and relaxing is the big difference in floating and not floating. (my experience)