Would the opposite sex hormones that Jazz had fulfil this function?
I'm not a biologist, but I don't think so. Not only is the male body not 'designed' (so to speak,) to make use of oestrogen in the same way as the female, but there are other hormones that are crucial to the female hormonal system.
Progesterone, which aids in proper breast development - the formation of the milk glands, the lobules etc, which in large part provide shape and mass to the breast. Tuberous breast deformities, where there is insufficient glandular tissue resulting in aesthetic issues, and which can affect females and males, seems to be rather common amongst trans males, and is what Jazz has. Given progesterone's role in breast formation, I suspect the reason for more trans males having it, might be lack of progesterone. Jazz did take progesterone for a short time to try to help their breasts, but it made them suicidal.
There's also FSH (follicle stimulating hormone,) produced by the pituary gland, which causes the maturation of a follicle in the ovary, follicles being what contain the eggs.
LH (luteinizing hormone,) which triggers the release of an egg from a follicle.
And even testosterone is very important to women, in the right amount, and important to energy, bone strength, libido, and wellbeing. All of these hormones interact and cycle as puberty begins, and will continue to do so until menopause.
This article explains it really well, despite being for kids:
When your body reaches a certain age, your brain releases a special hormone that starts the changes of puberty. It's called gonadotropin-releasing hormone, or GnRH for short. When GnRH reaches the pituitary gland (a pea-shaped gland that sits just under the brain), this gland releases into the bloodstream two more puberty hormones: luteinizing hormone (LH for short) and follicle-stimulating hormone (FSH for short). Guys and girls have both of these hormones in their bodies. And depending on whether you're a guy or a girl, these hormones go to work on different parts of the body.
For guys, these hormones travel through the blood and give the testes the signal to begin the production of testosterone and sperm. Testosterone is the hormone that causes most of the changes in a guy's body during puberty. Sperm cells must be produced for men to reproduce.
In girls, FSH and LH target the ovaries, which contain eggs that have been there since birth. The hormones stimulate the ovaries to begin producing another hormone called estrogen. Estrogen, along with FSH and LH, causes a girl's body to mature and prepares her for pregnancy.
.kidshealth.org/en/teens/puberty.html
Jazz, however, has blocked the effects of FSH and LH from doing anything to their testes via testosterone. And they have no female reproductive system of course, for FSH and LH to work on. Also, without a female reproductive system, all oestrogen does is form breasts, decelerate height growth, and reduce muscle mass.
How all this affects the brain is uncertain, but it seems clear that blocking androgens completely, while not allowing an actual puberty but only giving oestrogen, cannot have the same effect on a person's physical (including brain, most likely,) development as natural puberty.
A lot of synaptic pruning (related to aiding in critical thinking etc,) happens in adolescence, for example. But honestly, no one knows yet what the complex interplay between puberty and its hormones and an adolescent's healthy brain development may be.