I believe this is an important first step towards making the Expr classes more traditional classes. The concept with _parameters, etc. has been causing issues in the past in the context of inheritance (not to mention the confusion around recursion errors and other things)

This change also further highlights a couple of anti patterns where some implementations set attributes on the classes without them being registered as parameters which poses challenges to serialization and tokenization

This needs #11835 since otherwise I cannot properly subclass Expr for the test