Ktor 3 client auto-instrumentation does not propagate trace context when used inside Ktor server

Describe the bug

When using the OpenTelemetry Java Agent with a Ktor 3 application, outgoing requests made via HttpClient inside a Ktor server handler do not propagate the trace context.

• Context.current() and Span.current() are valid inside the server handler
• However, the outgoing Ktor client request does not include a traceparent header
• No CLIENT span is created for the outgoing request

The Ktor client instrumentation module is applied according to debug logs.

Steps to reproduce

Minimal JUnit test:

@Test
fun `ktor client inside ktor server does send traceparent`() = testApplication {
    var receivedTraceparent: String? = null

    val stubPort = 9090
    val stubServer = embeddedServer(CIO, port = stubPort) {
        routing {
            get("/tracing-test") {
                receivedTraceparent = call.request.headers["traceparent"]
                call.respond(HttpStatusCode.OK)
            }
        }
    }.start(wait = false)

    val outboundClient = HttpClient(CIO)

    try {
        application {
            routing {
                get("/trigger") {
                    val currentSpan = Span.current()
                    val traceparent = Context.current()

                    println("Current span valid: ${currentSpan.spanContext.isValid}")
                    println("Current traceId: ${currentSpan.spanContext.traceId}")
                    println("Current traceparent: $traceparent")

                    outboundClient.get("http://localhost:$stubPort/tracing-test")

                    call.respond(HttpStatusCode.OK)
                }
            }
        }

        val testClient = createClient {}

        testClient.get("/trigger")

        println("Received traceparent: $receivedTraceparent")

        assertNotNull(receivedTraceparent, "traceparent should be propagated")
    } finally {
        outboundClient.close()
        stubServer.stop(1_000, 2_000)
    }
}

Expected behavior

• A CLIENT span should be created for the outgoing Ktor request
• The traceparent header should be injected automatically

Actual behavior

• No CLIENT span is created
• No traceparent header is sent

Javaagent or library instrumentation version

2.26.1, 2.27.0

Environment

JDK: 21
Kotlin: 2.3.21
Ktor: 3.4.3

Additional context

No response

Tip

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Start with the minimal JUnit test in the issue and reproduce the request using Ktor 3's HttpClient inside a Ktor server handler. Check the Ktor client instrumentation behavior when the server context is active, using the debug logs and assertions for the CLIENT span and traceparent header. Done means the outgoing request creates a CLIENT span and propagates traceparent.