How to power WeMos D1 Mini without USB?
As I could understand from your schematic you are trying to use a D1 Mini to drive a 12V relay. But, the d1 Mini will not be able to drive a 12V relay and you are trying to use the darlington to do so.
Your d1_mini should be isolated from the 12V source. Which is most likely what is frying it. For that, you could use different approaches. But, the one that comes to my mind is using the d1_mini to drive a MOSFET. The MOSFET Drain -&gt; Source would be the one to provide the 12V required by your relay to activate.
Take a look at this video https://www.youtube.com/watch?v=FrpYtBeKzKk. It shows how to implement it using a single power source(https://youtu.be/FrpYtBeKzKk?t=32) or using different power sources(https://youtu.be/FrpYtBeKzKk?t=43).
In your case, you have virtually, 2 power supplies. Although using the same battery, there is power supplied by the battery and power supplied by the buck converter. Which could be illustrated by the image in the external power supply mode. https://youtu.be/FrpYtBeKzKk?t=48
So, I think you tried to do the same with the darlington but I could not see it as a good way of doing so once the darlington in my opinion has different purposes