You got everything right the first time ;-) The PEP is an extended illustration of "although that way may not be obvious at first unless you're Dutch".
I too thought "why not else:?" at first. But "case _:" covers it in the one obvious way after grasping how general wildcard matches are. Introducing "else:" too would be adding a wart (redundancy) just to stop shallow-first-impression whining.
"|" is also a fine way to express alternatives. "case" has its own sub-language with its own rules, and "|" is widely used to express alternatives (whether in regexps, formal grammars, ...). Spell it, e.g., "or", and then I wonder "what does short-circuiting have to do with it?". All reuse of symbols carries baggage.
".NAME" grated at first, but extends the idea that dotted names are always constant value patterns to "if and only if". So it has mnemonic value. When context alone can't distinguish whether a name is meant as (in effect) an lvalue or an rvalue, no syntax decorations can prevent coding errors. Names in destructuring constructs are overwhelmingly intended as lvalues, so adding extra cruft to say "no, I meant rvalue" is the pragmatic choice.