Kumar Use trace
policy to add custom trace to request tracing output and this creates a Trace telemetry in App Insights based on severity level. Check out doc: Trace for more info on this (Policy scopes: global, product, API, operation) and you can apply this policy at the global level so that you don't have add it in each API.
Currently, it is not possible to add custom data to App Insights without writing policy. If you have any feedback or suggestions, you can directly submit to our product team via https://aka.ms/apimwish and others with similar interests can upvote your idea too. I hope this helps with your question and let me know if any other questions.