Again, that's simply not true. That's not how copyrights work. Take Project Gutenberg for example- Project Gutenberg hosts public domain work. The copy of the work is still under public domain. What's not under public domain is the fact that PG hosts the public domain work.

For example, you wouldn't be able to use Archive.org's trademarks to advertise public domain work. But Archive.org does not gain hold a copyright over a copy of public domain work

So Getty images has a whole lot of photos of the paintings in the Sistine chapel. I bet those photos are copyright the photographer, ‘yeah but that’s because it’s Getty, that’s allowed’

You seem to be very confused. Getty pays photographers for the rights to their photographs.

Taking a photograph is creation of a new copyrighted work under some now-very-old United States Law. The key idea is "transformation": it's understood that photography includes an editor's eye of what is worth taking a photograph of.

Making a copy of a public domain book does not create an independent claim of copyright to the contents of the book. You can make a case that maybe it should, but it legally does not; that's just not how it works.

That's not how copyright law works.