Empty body sent when using Http4sBackend with circe JSON body with JdkHttpClient

[astridej]

Minimal example to reproduce

import cats.effect.{IO, IOApp}
import io.circe.Encoder
import org.http4s.circe.CirceEntityCodec.*
import org.http4s.jdkhttpclient.JdkHttpClient
import sttp.client3.*
import sttp.client3.circe.*
import sttp.client3.http4s.Http4sBackend

object Main extends IOApp.Simple {
  case class Test(foo: String) derives io.circe.Encoder.AsObject

  override def run: IO[Unit] = {
    for {
      client <- JdkHttpClient.simple[IO]
      sttpBackend = Http4sBackend.usingClient(client)
      req = basicRequest.put(uri"<some uri goes here>")
        .body(Test("bar"))
      _ <- req.send(sttpBackend)
    } yield ()
  }
}

Despite the fact that we set a request body, it is not sent to the server. If we set the JDK client logging to log requests and headers, we see it is sending a Content-Length of 0:

Oct 11, 2023 5:31:06 PM jdk.internal.net.http.Http1Request logHeaders
INFO: HEADERS: REQUEST HEADERS:
PUT / HTTP/1.1
Content-Length: 0
Host: <uri>
User-Agent: Java-http-client/21
Accept-Encoding: gzip, deflate
Content-Type: application/json; charset=utf-8

Cause

A coworker and I spent some time debugging this because it was so surprising. The cause seems to be the fact that the Content-Length header is not generated when you add a body using the circe BodySerializer (unlike if you set a raw string body). This then produces a http4s request without content-length header, which is passed to the JDK http client via the http4s wrapper. The JDK client in turn seems to have a problem where it needs all the content headers to be present: it somehow falls back to 0 content-length and does not send the body. (This was true on all versions of Java I tried.)

I admit that I'm not sure what point in the chain would be the right place to start fixing this, or whether a similar issue might affect any other backends that end up using a JDK http client in the end.