Hi @Adam Taylor Thanks for reaching out. I tried inhouse but i am unable to reproduce the issue I am able to see Logic apps in the list and this should actually work for consumption based Logic app. Could you please capture the .HAR logs (browser trace) to investigate further.
Reference: https://learn.microsoft.com/en-us/azure/api-management/import-logic-app-as-api#prerequisites
To take the trace please refer: https://learn.microsoft.com/en-us/azure/azure-portal/capture-browser-trace