Hey @Christian-SaschaNa ,
Without much context on how this integration is used, here is my 2 cents - you would have to also migrate the authentication method in original integration first and then test. For example, if your integration is with a third party tool, you would need to replace the authentication method to OAuth S2S from JWT first, then test and if everything is working fine, you can remove old credential. One way to see if the integration is working is looking at the API calls under Insights tab.
Hope this helps!
Best,
Isha