Facebook: Can Friends & Followers know what you Share in a Group Chat?

Your personal FB Profile has some Friends and Followers. Then that same personal Profile of yours is a member of a certain Group Chat (not Group), but the Friends and Followers are not members of that Group Chat.

So if you use the Share function of FB and share a post, a reel, a pic (from the FB platform itself) to that Group Chat, would your Friends and Followers know that in fact you shared something to that Group Chat, or even just a general something, like say “John Doe has shared this <reel> to a Group Chat”. Would such appear on their feed, notification, or somewhere else in FB?

I’m thinking of creating a separate Page, and then use that Page to share stuff (from the FB platform itself) to a Group Chat, to maintain my privacy from my Friends and Followers regarding that Group Chat. But I don’t know if a Page is even allowed to join a Group Chat. Again “Group Chat” and not “Group”, which are not the same. If this is allowed, please let me know too.

Thanks in advance.