[Additional info]
I tested previous versions one at a time and found that version 1.6.0 worked as expected. The issue began in version 1.6.5, and I couldn't find any versions in between to test. In version 1.6.0, the download list is cleared whenever the files are deleted, renamed, or moved. Ideally, this list should also clear upon exiting private mode.
I move all my files from the default download location to an SD card, which causes the download list to clear and achieves the same result, saving me from manually deleting entries one by one.
For now, I will continue using version 1.6.0 and refrain from updating the app. I hope this issue can be resolved soon, as the app currently states “private tabs and data cleared” when leaving private mode.