Here is an image of the sub selection tool:
How do I unselect this tool after I am done using it to adjust the vector shape?
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or to merely unselect the selected art...
Select > Deselect
Or just click anywhere else to deactivate the current selection.
The shortcut comes in very handy if you are zoomed in and there's really no "clear" area to click. But most often... I simply click a "blank" area in the document.
The shortcut also works in InDesign
What I do in your particular case, when I'm done editing anchors with the A tool, I switch to a 'low action' tool by hitting either: