struct type is unbound when declared inside a let

#lang typed/racket
(let ()
  (struct s ())
  (ann (s) s))

Gives:

Type Checker: parse error in type;
 type name `s' is unbound in: s
Type Checker: cannot apply a function with unknown arity;
 function `s1' has type Procedure which cannot be applied in: (s)

The second error is due to the fact that the constructor s has type Procedure instead of (→ s). This can be seen by writing (let () (struct s ()) s) at the REPL.

Reproduce the two examples in a Typed Racket REPL, especially the local struct declaration inside let and the standalone constructor expression. Trace how local struct bindings are parsed and typed; done means the type name is bound in the annotation and the zero-argument constructor receives the expected function type.