Add a baggage test to AbstractHttpServerTest, probably could leverage https://github.com/open-telemetry/opentelemetry-java-contrib/tree/main/baggage-processor#usage-with-sdk-auto-configuration (which is included in the Java agent already) in order to stamp the baggage on to the spans which could be used in the verification step.
A second baggage test could be added that sends two headers in order to test #12868.