LibreTube has a feature that no other piped/invidious client has, which is to have one auth instance and one view instance.
Sometimes videos are not viewable on a specific instance, but this way you can keep all your subscriptions and other settings even when switching to a different instance.
If I understand what you are saying, Piped has this. For example I can stream from instance-1.com but at the same time I'm logged into instance-2.com so that I can keep my favourites and settings. See "Instance" section here https://piped.video/preferences particularly the option "Use a different instance for authentication"
In my case at least, I can solve this by changing instance in the settings, as explained in my previous comment. Based on my experience, it seems that the less popular instances tend to have less frequent errors. Your mileage may vary though.
https://libretube.dev/