So, busyness is not a word. I know this. I’m aware. The question is, is there a relation between business & busy-ness? If not, there should be.
From www.etymonline.com:
It seems there is a link
There is. From the OED:
The various meanings of busy-ness are all obsolete.
Consider etymonline bookmarked. Thanks for coming through with the OED as well. Always the last word.