I've found that I bounce between coding at home, learning a new hobby, exercising more, building out a non technical skill, or just taking a period of R&R where I'm not actively trying to really accomplish anything in my off hours. The best engineers I've come across are this incredible balance of coding skills and perspective, and that perspective can be acquired in so many different ways.
You state that your ultimate goal is to learn and build things- Perhaps you could take the next four weeks and pick up crocheting or knitting. Or, buy a hard lego set and take a week and build out something in the physical space. Pay attention to what you're doing as you complete your tasks, and the ways in which your brain is coming up with optimization to make you move more quickly and efficiently. Now, think about how you could reapply those learnings in your development process or software design. Are there metaphors? Can you draw connections?
There are software lessons to be learned all around us. Don't fight the burnout. Pivot.