web-server/servlet/web seems to inhibit stateless operation

I had a rough time getting stateless servers to work. The culprit appears to be web-server/servlet/web. Include it and stateless does not work, exclude it and it works quite seamlessly on a non-trivial system. See

https://discord.com/channels/571040468092321801/1128483815787077692

for a small, illustrative example, reproduced below.

However, I don't see anything in the documentation for either stateless or web-server/servlet/web that indicate this. It should be documented in both places.

Sample program:

#lang web-server

(require web-server/servlet-env
     web-server/servlet/web)

(define (start req)
  (println "starting")
  (let ([r (send/suspend
        (lambda (k-url)
          (response/xexpr
           `(html
         (body
          (form ([action ,k-url])
            (input ([type "text"] [id "uid"] [name "uid"]))))))))])
    (println "there")
    (let ([uid (extract-binding/single 'uid (request-bindings r))])
      (if (member uid '("hello"))
      (response/xexpr `(html (body (p "yes"))))
      (response/xexpr `(html (body (p "no"))))))))

(serve/servlet start
               #:listen-ip #f
               #:stateless? #t)

Start by reviewing the documentation for stateless operation and the web-server/servlet/web module, then compare it with the reproduced sample using #:stateless? #t. Document the interaction and its practical effect in both relevant locations. Done means both topics clearly describe this behavior and the sample provides enough context to understand it.