Application insights for Azure Function on Kubernetes

Description of the issue

We're trying to migrate our infrastructure to Kubernetes. That also includes migration of function app. We've manage to do it succesfully, we have a working azure function, however there is a problem with application insights. Namely, it is not working. We don't see any logs not to mention distributed tracing which are vital for us. Is there a way to instrument Java function app insight hosted on kubernetes cluster?

Investigative information

Java version: 11
Here I'm posting a sample configuration from the environment variables of kubernetes deployment:

        - name: APPINSIGHTS_INSTRUMENTATIONKEY
          valueFrom:
            secretKeyRef:
              name: external-secrets
              key: secret-value
        - name: APPLICATIONINSIGHTS_INSTRUMENTATION_SPRING_SCHEDULING_ENABLED
          value: "false"
        - name: APPLICATIONINSIGHTS_PREVIEW_OTEL_API_SUPPORT
          value: "true"
        - name: APPLICATIONINSIGHTS_ENABLE_AGENT
          value: "true"
        - name: XDT_MicrosoftApplicationInsights_Java
          value: "1"
        - name: ApplicationInsightsAgent_EXTENSION_VERSION
          value: ~3

Dockerfile for the image:

FROM mcr.microsoft.com/azure-functions/java:4-java11-core-tools AS installer-env
COPY settings.xml /root/.m2/settings.xml
COPY . /src/java-function-app
RUN cd /src/java-function-app && \
    mkdir -p /home/site/wwwroot && \
    mvn clean package && \
    cd ./target/azure-functions/ && \
    cd $(ls -d */|head -n 1) && \
    cp -a . /home/site/wwwroot

FROM mcr.microsoft.com/azure-functions/java:4-java11

ENV AzureWebJobsScriptRoot=/home/site/wwwroot \
    AzureFunctionsJobHost__Logging__Console__IsEnabled=true

COPY --from=installer-env ["/home/site/wwwroot", "/home/site/wwwroot"]```