I use private browsing a lot for the automatic site data clearing. Several browsers restrict taking screenshots in private windows, which is only an inconvenience to me. I hope more browsers will allow the user to decide if screenshots are allowed on their own device.
Maybe Firefox Focus is what you are looking for. I use it to prevent random links from polluting my browser history. And seems to allow screenshots.
Yep, I did use to use Focus exactly for this purpose. At some point I switched to the DuckDuckGo browser for the same purpose, and that works well, too.