You pick up ANY colour. There doens't have to BE any decision-making, apart from "pick up the pencil and start making a mark on the page". Even young toddlers can do that, they are doing very little executive decision-making there, about what colour to pick. You could even just close your eyes and pick up a pencil.
To be honest, what you've described about yourself sounds more like a form of depression or maybe more general overwhelm which feels like there's no way out of. Which yes, can start after severe fatigue while recovering from a physical illness. Most of us, for example, know what it feels like to be off work ill or after an operation for more than a week. It can feel really daunting returning to work, you feel out of the loop, scared to put yourself back out there. Your heart races, you feel like the new girl again, you tell yourself you can't do it, everyone has forgotten you, no-one has missed you being there, you can't remember how to even log in to your computer, you wonder how you can get through the day without a snooze after lunch like you've been used to, how you will cope with the early starts when you've been used to getting up after enough sleep, how will you cope when you have to rush your lunch break.
If you're a woman of perimenopausal/menopausal age with hormones already creating havoc causing all the usual, often severe, menopausal anxixety and brain fog and fatigue, with even a small amount of neurodiversity on top, then it can feel insurmountable. Add on the stress of being in a high-level or pressurised job, with a lot of responsibility or deadlines, perhaps some past severe trauma that you haven't ever dealt with properly, and it all feels like not just a mental impossibility but an actual physical one, with real physical symptoms.
I think that long covid DOES exist, and can maybe flare up and down when your immune system is under attack, but I think that in a lot of people who have it, then all the other stuff above can just make it feel so much worse.