For me, the opportunity cost of being burned out is that I can't summon the energy to work on my side projects and hobbies. It really kills me that every day I come home and have hours that I could spend coding or building something, but instead I just watch TV over a beer.
A couple of people closest to me say to just do all the things. So they are advocating discipline which is great and something I could probably find again if I was more disciplined.
My gut feeling though is that the issue might be more complicated than that. From prior experience, I know my odds of failure at any side project I attempt are somewhere around 90% if I measure them in terms of monetary gain. So I'm subconsciously multiplying the cost/benefit analysis by 10 and getting discouraged. But if I remove risk from the equation, maybe by working on something low-risk like an open source project or learning a skill I don't know (like playing music), then maybe I could get closer to feeling rewarded by tinkering instead of drained. Then I could build on that and add more ambitious projects over time (in theory).