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.
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"