@iblamedoctors Hey, I got some experience with that; I used to be called Quasimodo for the bigger part of my life, in reference to my extremely poor posture.
Not sure if anyone cares, but to properly explain, I will give some context.
Doctors and physicians either told me it was for "bone structural" reasons or "genetics." Basically, I was told everywhere that it can't be changed.
After various trials and errors with stretching and mobility exercises recommended by "experts," I was about to give up because nothing worked. That day, before sleeping, I looked in the mirror, and I started flexing hard; for about 1-2 seconds, my posture was almost alright to look at.
That's where I got this idea: What if I had the strength to do this 24/7?
So I got into bodybuilding with an end goal of getting into athletics. I did some intense training. And sure enough, my hopelessly bad posture went not only away but also, sometimes, I even get told that my posture is good.
Needless to say, I got taller, and I also feel much taller. However, there was one problem, which was balance.
25 years of my life spent with an extreme hunchback did require some serious relearning how to even walk properly.
Which in turn got me into barefoot shoes, basically walking barefoot exclusively all day. This improved my posture again significantly. I may not be the most objective judge for myself, but I think it looks somewhat like Superman or similar strong people. In another year of training my upper back and using barefoot shoes, it's probably close enough to perfect.
Now to the downsides, which should be mentioned,
Depending on how bad your posture is, there will be quite a lot of pain, since strong enough muscles will almost forcefully put your spine in the right place. This can be addressed by supplementing with any type of mobility or stretches. Eventually any pain will subside, and your back will feel better than 99% of people ever will.
Walking barefoot should be done in increments, especially at the start; the risk of getting seriously injured is substantial if you overdo it.
Barefoot shoes basically give no additional height at all. This means everyone will walk around with +2-5 cm (0.8–2.0 inches). Meanwhile, you will have about +0, which, of course, makes you feel like everyone has suddenly gotten much taller.
The upsides
It can be done. Getting a better posture is quite simple but by no means easy. It takes years. If you're younger than me, it will likely be faster, but you still have to put some effort in.
Improved posture often comes with increased balance, like, for example, if someone doesn't pay attention and walks into you. You can be the guy asking, "Are you alright?"
Aside from getting taller, I personally think the main benefit lies in how you appear to the world around you and also how you feel. People perceive you as being more respectable, which naturally increases your own confidence.
If anyone cares for some more details, I'm willing to take the time to reply.
TLDR:
Do strength training; focus on the upper back. Get yourself some Barefoot shoes, but be careful not to overdo it. Be patient; as long as you make continued effort, you will eventually get whatever you want. Don't pay attention to people kicking rocks while you stack bricks.