Hello @Fabian ,
Thank you for reaching out to the Microsoft Q&A platform. Happy to answer your question.
As you confirmed the guest agent is running on the new machine, you don't have to make any further changes on the guest agent files. As long as there are no issues with connectivity you don't have to worry.
If you wish to continue with the new VM and remove old VM, there is no need to debug the issue any further.
Important to note:
When you deploy the VM from market place the guest agent is installed along with the OS. Sometimes there would be some issues during the updates that may cause VM agent to go unresponsive and shows not ready in status. In such cases, you can try to reinstall the guest agent as per the guidance available at the following link
https://learn.microsoft.com/en-us/azure/virtual-machines/extensions/update-linux-agent
Hope this helps :)
Please "Accept as Answer" and Upvote if the answer provided is useful, so that you can help others in the community looking for remediation for similar issues.