yt-dlp is generally the best open source tool for downloading/backing up videos from the internet. Despite the name, it works with thousands of video streaming sites, not just youtube. Completely free. I would never pay for a video downloading software.
It is command line based though. I’m sure there are forks with a UI, but I’m not familiar with them. There is a fairly detailed wiki for it, and a discord support channel. The defaults are fine for youtube back ups.
I would reccomend uploading whatever you back up to the Internet Archive. Then you aren’t responsible for hosting, and it’s available to the public.