Does pure OTel tracing work without tracing package?

[RolandColored]

Bug description

I'm running request-tracing with opentelemetry_0_31 flag and doing pure OTel tracing so far. But I struggle to get outgoing requests properly annotated with a trace id.

To Reproduce

let tracer = global::tracer("foobar");
let url = format!("{service_url}/endpoint");

tracer.in_span("fetch_foo", async |_cx| {
    let client = ClientBuilder::new(reqwest::Client::new())
        .with(TracingMiddleware::default())
        .build();
    let response = client.get(&url)...
});

Expected behavior

OTel headers should be injected into the HTTP headers, but none to be found.

Environment

Linux & Mac

Additional context

I debugged into otel.rs - fn inject_opentelemetry_context_into_request and noticed that call to

let context = Span::current().context();

yields a None span. Span references the tracing package, which is not configured in my case. So I wonder if the tracing package is actually a hard requirement?