OP, I am in a similar position as your wife. I also have several neurological conditions that require high-powered medications, none of which are safe for use during pregnancy. So my options for having a bio child were go off the meds & risk pain/stroke/death, or stay on the meds & risk having a stillborn child (or having a living child with severe birth defects.) So, not really much choice there. Besides, my health conditions are genetic (several people in my family have them), so tbh my DNA was not exactly something I wanted to inflict on a hypothetical child anyhow.
My husband & I proceeded with adoption, despite all the horror stories we'd heard. Well those stories exist for a reason, and our plans fell through. We had no more money to pursue other options (like surrogacy with donor eggs/sperm), and I really didn't have the heart to be crushed again. Still, it's tough when people tell you you'll never be a real woman until you've had a child, or now you'll die alone with no one to take care of you. We learned quickly to cut those toxic people out of our lives, but their words still stay with me (even after years of therapy.)
I offered my husband a divorce to allow him to find a less defective woman (as that is exactly how I saw myself), but he flat out laughed at the thought. For him, keeping our existing relationship was more important than trying for a hypothetical child. He has never once blamed me for not being able to give him a baby. In fact at this point, he has fully embraced being childfree! It took me longer to come to terms with never being a mom, but I'm at peace with it now. I'd like to think my life is happy & full regardless - it's just happy & full in a different way than the one I originally imagined, which required me to think outside the box (as it were) and do some intense soul searching that would otherwise never have happened. My point is that it's completely possible to find happiness & fulfillment even if you don't get your wish - you're not doomed to a lifetime of sackcloth & ashes by not being a father.
So OP, you need to think outside the box now. Who is more important to you, your current wife or a hypothetical new wife + hypothetical child? Does the reality of fatherhood appeal to you, or just the idea of being a father?
Being the first born son in my family means I'm expected to provide the next son, and I want to do that
I'm sure you realize there's no guarantee of this actually happening, so this comment strikes me as you being in love more with the dream of a child rather than the reality. If you choose to stay with your wife, you will need to adjust your dreams & imagine a different kind of happy life for the two of you.
That said, if after much soul searching you decide that having a biological child is the most important thing in your life, you will either have to 1) take out a loan to afford a surrogate, or 2) divorce & hope you find another woman willing & able to provide you with offspring. Keep in mind option #1 has plenty of risks involved, and there's no way you come out looking good with option #2. This is the reality of your situation.
TL;DR - Your ultimate happiness in this situation is based more on your own mindset than your circumstances. Changing your outlook may be the most viable option in the long run.