Yes And no dig is also about allowing fungi to work with roots, it’s a wonderful and complex system, enabled by us leaving alone.
I can’t answer your green manure question as you do not say what the plants are. Nor do you say what proportion of your bed is filled with soil.
If it’s all soil then I would scrape some off
Before adding compost.
Otherwise as Don says, compost consolidates to a small volume, quite quickly.
