Hi,
The Elastic APM agent does not have support for Grizzly, and Jersey might be used without the Servlet part (which we do support), which might explain the issue you are facing here.
Maybe as an alternative could you try to use the OpenTelemetry Java agent that seem to have some support of Grizzly: GitHub - open-telemetry/opentelemetry-java-instrumentation: OpenTelemetry auto-instrumentation and instrumentation libraries for Java
However, I can't check if that will work as expected in your case, as I don't have a similar application, thus you'll have to try it yourself here.
For the configuration of the OTel agent, you should be able to get proper instructions near where the Elastic agent configuration is available in Kibana (where you get the -javaagent argument and configuration variables), also the general OTel guide might be relevant as well)