Tracing for stdlib http.HTTPServer

Describe your environment

OS: Fedora 41
Python version: 3.13
Package version: 0.49b2 / latest

What happened?

A simple app is not instrumented properly

from http.server import BaseHTTPRequestHandler, HTTPServer

class RequestHandler(BaseHTTPRequestHandler):
    def do_GET(self):
        if self.path == '/':
            self.send_response(200)
            self.send_header('Content-type', 'text/plain')
            self.end_headers()
            self.wfile.write(b'Hello')
        else:
            self.send_response(404)
            self.send_header('Content-type', 'text/plain')
            self.end_headers()
            self.wfile.write(b'not found')

def run(server_class=HTTPServer, handler_class=RequestHandler, port=8080):
    server_address = ('', port)
    httpd = server_class(server_address, handler_class)
    print(f'Starting server on: {port}')
    httpd.serve_forever()

if __name__ == '__main__':
    run()

Steps to Reproduce

And instrument

pip install opentelemetry-distro opentelemetry-exporter-otlp
~/.local/bin/opentelemetry-bootstrap -a install
~/.local/bin/opentelemetry-instrument  --service_name python-example  --exporter_otlp_endpoint localhost:4317 --traces_exporter console,otlp --metrics_exporter console python helloworld.py
...
Starting httpd server on port 8080
127.0.0.1 - - [02/Dec/2024 13:59:40] "GET / HTTP/1.1" 200 -
127.0.0.1 - - [02/Dec/2024 13:59:40] "GET / HTTP/1.1" 200 -

Follow steps in https://github.com/pavolloffay/otel-python-bug-03969593

Expected Result

See traces from HTTP server

Actual Result

No traces reported, no logged error in the app.

Additional context

https://github.com/pavolloffay/otel-python-bug-03969593

Would you like to implement a fix?

None

Reproduce the report with the linked repository and its helloworld.py HTTPServer example; start at the opentelemetry-instrument entry point and Python's stdlib HTTPServer. Compare the run with the expected console or OTLP output, and consider it done when HTTP requests produce traces without application errors.