Why not real anonymous functions?

The current lambda is a particular implementation of anonymous functions. It is possible to imagine implementing anonymous functions in a way that does not build on the current lambda implementation at all. However every proposal and consequently every objection seems to assume that what we need is to extend the current lambda implementation to support mutliple statements (as you say, “multi-line” is not precise enough, but that does appear to be the terminology).

I’ll double down on this point, as it is the crux of my original question: where have anonymous functions been proposed? I genuinely don’t see anywhere that someone has said “let’s add real anonymous functions to Python”. Truly I expected to find a rejected PEP. At least part of my question is: why is there not even a PEP for this?

I’m slightly frustrated because everyone here seems to be aware of some deep history on this topic. But as a relative outsider there’s very little official documentation on something that seems like a major potential benefit to the language. It would be perfectly reasonable to expect to see a PEP outlining why Python can’t/won’t do this. But there is no such thing; just a variety of arcana about why “multi-line lambdas” won’t work.