The initial happiness (first two weeks) is mainly from euphoria - knowing it’ll improve from now on, is a huge thing.
I think for a cis guy a slightly stereotypic parallel might be if you felt somewhat blue during your teen life that you can’t quite grow a moustache yet. Or not looking like one of those muscular guys. But knowing you eventually can likely grow the moustache/muscles - that gives you happiness as something to look forward to.
And for a cis gal, it might be the mental dissatisfaction with one’s own body when on period (not to confuse with the physical period symptoms). I feel that that might be a similar thing to dysphoria, though of a more temporary nature.
But, the thing is that for us trans people, this dysphoria/euphoria feels significantly stronger.
That’s often because all the time that we didn’t realise or were unable to transition, the body development and expression feels like going the wrong way. Like an everyday “ugh” feeling, not quite happy. And so - to give a crude example - when we finally get that sweet hormone, it’s like the mental trance relief you feel from finally being able to pee after a long movie.
After those initial weeks, the euphoria mostly strengthened as just a general feeling of being able to feel like your happiness isn’t faked - more genuine.
Some take HRT (hormone replacement therapy, ie. getting onto estrogen/testosterone), others don’t. Some don’t have surgery and others don’t change literal clothes but others do. Any of that is fine, the important thing is feeling happy and comfortable in your body. And I very much do now!
It varies, but I think the feeling of euphoria vs dysphoria I described is more or less similar to what others have.
Oh and, thank you! Yeah, the hormones have a massive influence on your body. Non-queer guys and gals often think it only tweaks a little here and there, but they do so much more.
You having thicker hair? More strength, oily skin and grip? Anger being easier to express? All testosterone, baby.
Softer skin? Sadness easier to express? Boobs and hips, butt, rounder face? Harder to grasp jars? Period?[1] Estrogen.
[1] they’re basically like stomach nausea but feel to be down around where your pee bladder is. And also sometimes like a hand is grasping the area tighter (without feeling like you need to go). This is because periods affect not just the uterus, but also the area a little around.