Your nucleus accumbens isn't necessarily very smart, and isn't necessarily segmenting its world into "work" and "not work". "Work" here is a poor term in this context, it's an English word and subject to a lot of ambiguity. It might be somewhat more accurate to rephrase that as "You are training yourself to believe that all effort is futile", effort towards anything, which is why you end up just staring into space. Or perhaps not, who knows what the truest truth is, I'm really more saying that I doubt that part of your brain sees "work" as you were using the term.

I think it depends on the individual and how they see work, how one aspect of their life leaks into another another and so on.

Speaking personally I know that even when I'm stressed at work I still know the difference between tasks carried out as part of my job, and tasks carried out which are potentially similar, and which may be being carried out in a work setting, but which are not work.

Don't get me wrong, if I feel work is going badly, doing something else and being OK at it is almost certainly a good thing, I just think that doing something work related and doing it well is probably better.

Not true. If you code and solve problems at work, and fail spectacularly, you don't want to try and solve more problems. The brain is very good at generalizing stimuli: having your code compile is like a programmer's own little Skinner box. So if you can find problems in other domains and solve them, you'll still enjoy programming and solving problems.

I do agree that you need some successes at work, though. If you were doing really well in private, but everything at work was going wrong that would cause problems.