How much battery does it actually say it is using?

I’m not sure that is too much out of the ordinary. Was that 5 hours of foreground time?

You could see what happens if you tell it to disable background usage. Privacy Browser should not be using any CPU in the background (it pauses JavaScript timers in the background), so disabling nonexistent CPU usage shouldn’t cause any problems.

Although, as you suggested, sometimes these messages are poorly worded. Perhaps it doesn’t like Privacy Browser consuming RAM in the background. Moving it out of RAM doesn’t typically save any battery power because, as I understand it, the RAM consumes the same amount of power whether or not there is data sitting in it.

If you run Clear and Exit when you are done with Privacy Browser, either through the Navigation menu or by closing the last tab, that should completely remove Privacy Browser from RAM as well as guarantee there is nothing left that could possibly use the CPU.