No, You do not delete the classic app insights. The main difference between classic app insights and the new one is that the new one is attached to Log Analytics workspace. You still have the resource for the app insights and you can use specific App insights features within it. Your old data will be available via the new query data in Log Analytics. From the docs "When you migrate to a workspace-based resource, no data is transferred from your classic resource's storage to the new workspace-based storage. Choosing to migrate changes the location where new data is written to a Log Analytics workspace while preserving access to your classic resource data." and also: Does migration affect AppInsights API accessing data?
No. Migration doesn't affect existing API access to data. After migration, you can access data directly from a workspace by using a slightly different schema.
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.