No, we don’t know that. Thats discussed very controversially in the scientific literature. For example re-evaluation of the NHANES III data using the CDCs standardized method revealed a mean T level of young, lean and healthy men of 624 ng/dL Samples were taken between 1988 - 1991 and that’s 3 decades ago. Essentially the same mean T level of the same group of men is measured nowadays - so this data suggests no decline in T levels happened within the last 3 decades.
The 25th percentile of young, lean and healthy men in 1990 was 516 and the 75th percentile was 751 ng/dL. If he brings his levels to 600 to 800 that corresponds to being in the upper part of the population with regards to T compared to young, lean and healthy men 3 decades ago.
We are still very early into the science of what’s causing different emotional/behavioral states. One interesting theory how T potentially impacts emotion is by interfering with the synthesis of neuroactive steroids. Basically T either directly modulates GABA receptor activation or it modulates synthesis of other neurosteroids which in turn modulates GABA receptor activation. There is some good data that demonstrates that GABA receptor modulation is at the center of the so called steroid rage type of behavior.
Some people just seem to be very sensitive to T messing with these neurosteroid pathways.
Essentially the only way to limit this effect is to reduce the T dose.
A maybe interesting option for you might be myo inositol. In the 90s a number of studies were done to investigate into the potential application of this substance for the treatment of anxiety disorders, ocd and depression. Essentially a couple grams of inositol were as effective as eg fluoxetine (an SSRI) and superior to placebo. Maybe worth a try.