JDownloader 2 will also do this.
Data Hoarder
We are digital librarians. Among us are represented the various reasons to keep data -- legal requirements, competitive requirements, uncertainty of permanence of cloud services, distaste for transmitting your data externally (e.g. government or corporate espionage), cultural and familial archivists, internet collapse preppers, and people who do it themselves so they're sure it's done right. Everyone has their reasons for curating the data they have decided to keep (either forever or For A Damn Long Time (tm) ). Along the way we have sought out like-minded individuals to exchange strategies, war stories, and cautionary tales of failures.
Like plunki said, YT-DLP will work. All you have to do is feed YT-DLP your playlist URL (if it’s private, I believe you’ll need cookies but if it’s set to unlisted, you won’t need them) and it’ll begin to download your videos.
I’d also highly recommend adding the argument “—download-archive archive.txt”; this will create a text file and log the videos you download so that when you run the command again later, it’ll skip all the videos that it’s previously downloaded and just download the new additions.
Only issue is that it isn’t automatic by default* so you’ll have to run the command every few days/week.
*While it may not be automatic by default, you could whip up a script that runs the command every few days or week w/o your input.
Stacher is a frontend/GUI for yt-dlp and has a "Subscriptions" feature that does this very thing. It works by creating an archive for each subscription and then, on the schedule configured, running yt-dlp with the configured parameters.
The official site is https://stacher.io and the subreddit is /r/stacherio
Yt-dlp does pretty much everything. It can do a channels playlists, not sure about a custom saved one, but try feeding it a link to it? Then you can just keep re-running it to download any new additions