I think part of the disconnect is that this enhancement could very easily be abused, and it seems likely that it will be, because the problems aren't visible while writing the code -- only when reading it later.
I therefore suggest making it very clear in the PEP -- and probably in PEP 8 -- how these expressions should be limited. Simply renaming them to "nickname binding" would be start, but here is a rough draft for wording.
When scanning code by eye, it is helpful that assignments are (almost) always at the start of a line. Even def and class statements can cause confusion if the reader didn't realize that the name referred to a class, rather than an instance. Moving assignments to the middle of a line will make it harder for someone else to read your code -- so don't do that.
A nickname is just a regular name, except that it also suggests an intimate environment. If the name is purely for documentation, or will be used only later in the same expression (or, possibly, the same block or just after), then a nickname may be appropriate. But
If you are wondering what to do about type hints, then the expression is probably too complex to leave inline. Separate it out into a regular assignment statement; nicknames do not support type hints.
If you will be saving the value -- even as an attribute on self -- there is a chance it will be retrieved in a very different context. Use a regular assignment statement; nicknames are just simple names, not attributes or keys.
If you will be using the value somewhere else in your code, use a regular assignment statement. This makes it easier to find, and warns people that the value may be used again later.