It worked for me just now, with Chrome. If you're on Linux, have you tried `mkdir /tmp/t234 && HOME=/tmp/t234 firefox` or creating a new local user and logging on as that user? It would be interesting to know why your private tab isn't working.
What did you try on Bloomberg? Opening bloomberg.com and clicking at the biggest, most central story shows me the whole story in full, both in Firefox and in Chrome in private mode. But clicking a random story in the sidebar (https://www.bloomberg.com/news/articles/2020-09-27/saudi-ara...) only gets me an abbreviated version in both browsers. Interestingly, it even customizes the message: "You're in private mode." in Firefox, "You're browsing incognito." in Chromium.
