You’re probably more of an expert but what you’re saying is totally unintuitive to me.

If a signal carries the “this looks like a signal” information in addition to the source information itself... isn’t that a waste of bandwidth? Wouldn’t an ideally encoded stream be indistinguishable from noise?

I can understand for practical reasons leaving some bandwidth on the table to make it easier to detect signals, but when talking about advanced alien life forms we have to assume they are playing closer to the limits of physics.