Quasisyntax inconsistently infers "Syntaxof Any" vs. Syntax

What version of Racket are you using?

v6.12

What program did you run?

#lang typed/racket

(: x Symbol)
(define x 'x)

(: f (-> Syntax Any))
(define (f x) (syntax->datum x))

(f #`#,x)         ; Syntax,       prints as 'x
(f #''x)          ; Syntax,       prints as ''x
(f #`(quote #,x)) ; Syntaxof Any, prints as ''x

What should have happened?

In the third call to f, the argument is inferred as Syntaxof Any. This can be narrowed to Syntax, as evidenced by the second call, which represents the same value but has a narrower type.

The corresponding S-expression version compiles:

#lang typed/racket

(: x Symbol)
(define x 'x)

(: f (-> Sexp Any))
(define (f x) x)

(f `,x)
(f ''x)
(f `(quote ,x))

If you got an error message, please include it here.

a.rkt:11:5: Type Checker: type mismatch
  expected: Syntax
  given: (Syntaxof Any)
  in: (quote (unsyntax x))

Start by running the provided typed/racket reproducer and comparing the three quasisyntax calls with the corresponding S-expression examples. Trace how the type checker infers the third call's argument; done means it is accepted where Syntax is expected without changing the intended inferred types of the other examples.