"missing type for identifier" / expression's type changes, with weird combination of requires and eval

Start with the supplied typed/racket reproduction at the REPL, focusing on the baz and bar modules, their begin-for-syntax blocks, eval call, and phase-shifted requires. Compare the first and repeated expressions, then the renamed-identifier and mylib/empty variants; done means repeated evaluations preserve the inferred type and no longer report a missing type for v or produce Any.

What version of Racket are you using?

6.9.0.1

What program did you run?

#lang typed/racket
(module baz racket/base
  (require (for-syntax racket/base))
  (begin-for-syntax
    (eval '0
          (module->namespace 'racket/private/sc))))
(module bar
  racket/base
  (require (for-meta -2 (submod ".." baz))
           ;; Bug also occurs with typed/racket/no-check here:
           (for-syntax typed/racket)))
;; Main module:
(require (for-syntax 'bar))
;; At the REPL of the main module:
#;(let ([v 1]) v) ;; First try works
#;(let ([v 1]) v) ;; Error on second try
;; Type Checker: missing type for identifier;
;; consider adding a type annotation with `:'
;;  identifier: v in: v

Splitting the file into several separate files still triggers the bug (but if I try to inline the require statements from bar into foo, shifting everything one meta-level up, then the bug stops occurring). If the second try renames v to w, then it works fine, but later uses of v or w trigger this bug.

If I use my type-expander in module bar, then I can trigger a slightly different bug: the type of the result of ((λ #:∀ (A) (x) x) 1) is Integer on the first try, and becomes Any on the second and later tries. If the second try renames x to t, then it works fine, but later uses of x or y trigger this bug.

#lang typed/racket

(module baz racket/base
  (require (for-syntax racket/base)
           (for-meta 2 racket/base))
  (begin-for-syntax
    (begin-for-syntax
      (eval '0
            (module->namespace 'racket/private/sc)))))

(module bar type-expander/lang
  (require (for-meta -2 (submod ".." baz))))

;; Main module:
(require 'bar)
;; At the REPL of the main module:
#;((λ #:∀ (A) (x) x) 1) ;; Type: Integer
#;((λ #:∀ (A) (x) x) 1) ;; Type: Any
;; More meaningful example of usage:
#;(let #:∀ (A ...) ([v : (List (Pairof Any A) ...) (list '(0 . 1))]) v) ;; (List (Pairof Zero One))
#;(let #:∀ (A ...) ([v : (List (Pairof Any A) ...) (list '(0 . 1))]) v) ;; (List (Pairof Any One))

Note that these bugs do not depend on the use of racket/private/sc. If I change it to mylib/empty, where the empty.rkt only contains (module quux '#%kernel), the bugs still occur.