What is the etymology of “business” and “busyness”?

“Why change an existing word, then create a similar one which means what the old one did? Why not just create a new word?”

Because, with very few exceptions indeed, language development is not done by a planning committee. Language evolves over time.

According to OEtmD, business is the modern spelling of the Old English bisignes “care, anxiety, occupation,” from bisig “careful, anxious, busy, occupied, diligent”. The meaning of this word eventually evolved to “occupation” and then “trade”. Thoreau may have been the one to coin the modern word busyness to mean “being busy”; he is given credit for the first use of it in 1849.

(This question reminds me of the story I read in an economics book, probably by David D. Friedman or Steven Landsburg: The Russian bureaucrat responsible for setting factory prices for raw materials was visiting the US and asked to meet with his counterpart. He was dumbfounded by the response: there isn’t one. He simply could not imagine a stable situation in which commodity prices were not set by a bureau but instead somehow governed themselves.)