I don't think I would agree that just because something is public that it's a public forum. I feel like the public has to own it as well. I looked it up and maybe it's because I predate social media by rather a lot, but I think of it in the classical sense:

Public forums are typically categorized into three types:

1. Traditional Public Forums: Long-established spaces like parks or sidewalks, where people have historically exercised their rights to free speech and assembly.
2. Designated Public Forums: Areas that the government intentionally opens up for public expression, such as town halls or school meeting rooms.
3. Limited Public Forums: Spaces opened for specific types of discussions or activities but with certain restrictions on the subject matter or participants.

The important factor being public ownership of the forum. I will concede that it has colloquially come to include public social media, but I think it's important to distinguish that it's not really the same thing at all as has been discussed through most of our history.

Food for thought. I just think calling them public forums attaches too much importance to a profit seeking endeavor.