Nope, you can see a condensed version of their acquisition history on their Wiki page for more proof: https://en.wikipedia.org/wiki/Atlassian#Acquisitions_and_pro...

When BitBucket was acquired they were cloud only, and when Stash launched it was on-prem only. We used Stash and BitBucket Cloud around that time at the place I was working and I can definitely tell you that on-prem Stash was definitely not a reskinned on-prem BitBucket Cloud; for one I’m pretty sure BitBucket Cloud was written in Python (Django) and Stash was a typical Atlassian Java product.