Oh I'm so sorry, he looked like he was doing great too...Please don't blame yourself, you did nothing purposefully to him, and as soon as you found out what needed corrected you went out and got it, and spent a good amount of money doing it...He could have had another underlying issue, or it could have just been the heat caused him to have temperature regulation issues, I've seen that before too. He definitely was not emaciated, he was taking in enough nutrition...He was just too small for his body to handle the stress, it's so difficult when they are that young and they become ill, their tiny little bodies just can't take it...but it's not at all your fault, I couldn't believe the way you ran out and got him every little thing he needed, plus some.
Whether you know it or not, that usually doesn't happen. The most common issue we see on this forum is people who buy their first baby beardie but they are given bad advice by the pet shop employees, even by the breeders sometimes, and they don't have any of the correct equipment, they almost always have the wrong
UVB light or no
UVB light at all, no thermometers, the wrong food, tank, etc., and then when we tell them the corrections that need to be made, they typically refuse to buy even the crucial things that they need to just survive, like a proper UVB tube...So it was quite obvious when you ran right out and got him absolutely everything he needed and then some, that you really loved the little guy and wanted him to have the very best of everything, and he did. So please don't feel guilty or anything, you did absolutely everything you could.
Look at it this way, you've learned a lot about caring for them, and you have an absolutely perfect set-up for another little beardie, so if you decide to get another baby you'll be ready to go and you'll know exactly what to do. I know that doesn't make this any easier and you cannot replace the little guy that you lost, but there's no shame in getting another baby. You'd not be replacing the guy you lost, just opening your family and your home up to another baby that needs a loving family.
If you need anything at all or have any questions in future, please do not every hesitate to ask..