I don't know if this is at all related, but I have found that I have to think of rest as being two different sorts: passive rest (i.e. sleeping, sunbathing, etc. typically "body" rest), and active rest (stuff that tends to use the mind, or are stimulating in some way). When I have been burnt out, I find it hard because I lack active rest, and it makes me super antsy. Sometimes I desperately need some passive rest (especially as I have some physical disabilities too), but my need for active rest can be so great that it feels torturous to engage in passive rest.

The worst is when I am too mentally burnt out for active rest, such as if I am ill, or if I hadn't been having to spend all my mental energy on work tasks. I think, for me, brain fog is related but distinct. To use an analogy, brain fog is like the drain of a bath being blocked; lots of people can experience brain fog, it isn't specifically an ADHD thing. The ADHD component here is like being unable to close the taps that are filling up the blocked bath. This means that ADHD + brain fog = the bath will inevitably overflow. This is what the agony feeling is to me. It's not the brain fog per se, but the inevitable consequences of the brain fog.