Does a word exist for experiencing the conflicting emotions of restlessness and ...

I am AuADHD and regularly experience a state of emotion where I am perfectly happy to be in a situation or activity, while also desperately itching to be doing something-- anything-- else. Does English have a word for this?

No, English has no word for that. Part of the reason is that your Exposition wholly denies the possibility in your actual Question.

Sorry if this seems harsh and unless you're willing to replace 'perfectly happy…' I don't think any of us needs professional qualifications to point out that what you describe is simply not possible.

Believing you experience an emotional state in which you are perfectly happy to be in a situation, while also desperately itching to be doing something - anything - else describes only your belief, not your actual emotional state.

If by 'perfectly happy…' you actually meant something like 'not too unhappy…' or 'reasonably content…' that might work but being 'perfectly happy to be in a situation…' and also 'desperately itching to be doing something else…' is simply not possible, for you or for anyone else. The two are by definition mutually exclusive.

Whether you can craft a better explanation on your own or only with help from a therapist, I won't try to guess.