"Greyed out"... After some serious research I found out why it was greyed out in my own docs and how to solve! Here it is.
I had lots of tracked changes, incl. ones that included the numbering etc. That seems to confuse Word. I accepted all changes around that numbered paragraph and...... instatntly the
"Restart at 1" re-appeared! Hoorah. SORTED!
Lesson learned: don't make it too difficult for Word, especially not with Tracked Changes!
What you are describing is a known limitation: As long as you are tracking changes, auto numbering and field results will not display properly. As you have noticed, accepting changes (and turning off the tracking) fixes it.
I believe the post to which you are responding discusses restarts in multilevel lists, though, not restarting via the right-click/context menu.