A related frustration for me is when I have random videos in my "watch later" list replaced with a gray square and a note saying the video is no longer unavailable or has been made private. Since I don't even get any details of what the video was (title/channel/description), I can't go find it elsewhere. It's like having a song deleted from a playlist silently. It makes me wonder if I should even rely on Google's features for this sort of thing, or maintain a list elsewhere.
In light on this common experience of natural and intentional link rot for YouTube videos, I think the only sensible strategy is to use youtube-dl to download videos to watch (and possibly delete) later.
Its all pretty seamless with rss too. You can set mpv to be your default browser for video links and it will scrape and start playing and you can save the video too. I use newsboat and a master script that uses some regex to figure out what to open the RSS link with (like a browser, feh for images, or mpv, or rtv for reddit links, etc)
Google the URL. You'll often find it in the Google cache or linked from somewhere else with the full description. This can sometimes be enough information to find an alternate source.
These days I use ytdl instead of watch later... A friend sent me a link to an amazing tech tutorial someone made and they wasn't sure whether that is their thing. Of course they received a lot of abuse from internet trolls and later deleted the video and disappeared. I was never able to find that video again and since then I always download.
Almost like submitting to centralized gatekeeping is a crime against public culture, intellectual history and social integrity... wait... what are we all building again?
We have already built a corporate dystopia where plebs spend their precious time making content which enables a giant multinational company to generate billions in advertising dollars.