Youtube [Data-API] LiveChat where logged-in user is moderator

I don't think the API supports a way to retrieve a list of chats where the logged-in user is a moderator. The liveChatModerators.list method requires that a value be set for the liveChatId parameter, and that value must specify a single live chat ID.

I'll caveat the following by saying that I'm not familiar with the apps you mentioned or how they work, so this is just conjecture. Your question describes a third-party app that lets you (or helps you to) manage YouTube live chats. Presumably, to use the app, you must have granted that app permission to manage your YouTube account.

With that in mind, if you set up a live stream through that app, then the app could, while creating the live stream, also use the liveChatModerators.insert method to add its own channel as a moderator to the live stream's chat. Similarly, the app could retrieve your list of live streams and add its own channel as a moderator to any of those live streams. The app could use its own data store to determine whether its channel had already been added as a moderator for any particular chat.

Please post a comment in reply if you don't think I'm understanding your question.