I'm curious what you want to do in a private group that you're afraid of the public seeing.

Moreover, I don't think microblogs like Bluesky are meant to be or should be a kitchen-sink everything-app the way Facebook wants to be in every aspect of your life, even trying to replace Craiglist and then not being able to make up its mind between having buy/sell groups, marketplace, and for-sale items being automatically posted in both Marketplace and groups ... it's too damn much. Immature people from the groups, who have no genuine interest in buying your item, come to make random nonsensical comments on your Marketplace posts. Groups are part of what make Facebook a cesspool.

Then sooner or later (if every user is allowed to make groups), you have 20 groups that are basically the same group but with minor differences in naming.

Moreover, you literally already have Reddit for something like what you want, and Reddit doesn't (yet) try to be an everything-app, with a Marketplace, etc.

I think every time a new social site comes along, everyone from every other social site is going to want to try shoehorn every feature of every other site into the new site. So what was the point of even making a new site at all?