It sounds like you are aware that you are scraping videos that are later re-labeled as "unlisted", but you don't mention what you do to mitigate this problem.
Even if it may not be illegal, at the very least it would seem un-ethical to link to private videos like this, and it would seem trivial for you to "re-scrape" your database every now and then to check whether any existing videos have changed from listed -> unlisted, and if they have, remove them.
Even if it may not be illegal, at the very least it would seem un-ethical to link to private videos like this, and it would seem trivial for you to "re-scrape" your database every now and then to check whether any existing videos have changed from listed -> unlisted, and if they have, remove them.