I have severely low testosterone. I've had a dozen blood tests and always come back in the 120 - 130s. I'm 34 years old. I figured it out on my own by piecing together the symptoms. Same issues as you had - Excess weight, no muscle, no endurance, very slow to recover from exertion, low sex drive, foggy brain, zero motivation and totally burnt out after a 9hr work day. My mental state has not been good for a long time. I don't have any friends or work on projects because I just don't have the energy for it after work and it takes me all weekend to recover enough to face the next week.
I am not currently taking any kind of treatment for it because my wife and I are not done having kids. HRT has a significant impact on fertility and I'm not willing to mess around with that. I've had my fertility tested and it came back normal despite my testosterone issues. We've had a lot of problems with fertility as it is, our first one took nearly a year to conceive and we've had a couple of miscarriages while trying for the second.
I'm fairly sure I've always had low testosterone, right since I was a teenager. My brother and father are both fit, active and highly motivated people. I've always been overweight with no muscle and no endurance. I have always had to put monumental effort into getting myself up and out the door every morning for work.
I'm hoping that our second kid is a boy so we can call it quits and I can start HRT. I think it is going to make a massive difference in my quality of life.