<<Sharing the information here from comments for broader community usage. Thank you>>
@Peter van der Veen Welcome to Microsoft Q&A and thanks for reaching out with your query.
For the scenario you have outlined , you have to write some custom code to ingest the telemetry needed into Application Insights , it would not be collected as out of box.
I came across this Stack overflow thread (answered by donquijote ) which talks about similar scenario, please review and see if that helps.
Additional documentation reference on Application Insights API for custom events and Metrics
Hope the above information helps, please review and circle back if you have any further queries. Thank you