Here is my experience: (50 Years old, overweight)
I started Testosterone therapy about 5 months prior to getting on CPAP. My T level was very low, (120). When diagnosed with sleep apnea, I had an AHI of 118.
That was almost two years ago -- now my AHI is averaging around 2-2.5 a night with CPAP. I have to get a T test every 6 months or so, and I am in the middle to low in my "normal" range.
About 6 months ago, I decided to forego my Testosterone therapy for a couple of weeks. During that time, I was still on cpap and my nightly AHI stayed around the same, but maybe a point /point and a half higher.
However, my Testosterone dropped significantly -- down to only 48, so i juiced back up and got it back in the normal range for myself.
I take T once a week, and what I noticed is that my AHI is slightly higher on the few preceding nights after injection, but gets back to average nearer the end of the week.
Just from my anecdotal experience,
Testosterone therapy may increase your sleep apnea. (This is a known side effect)
Sleep apnea made me extremely tired and listless, so I believe that was a causing factor in my low T, not from OSA
Now, I have also recently started exercising regularly and have adopted a plant based diet (for the most part). On my last T test, my levels were a lot higher -- also, my libido and stamina lasts a lot longer than it did before.