Dear Gkouk,
Thank you for posting in Microsoft Community.
I understand that you have an issue on SharePoint Task Lists not syncing with MS Project when approvals are activated. Before moving forward, we need more detailed information about the situation you are experiencing.
Kindly share with us the information below:
How many task lists are affected.
Content approval works only online and the lists will be on read-mode only once this feature is enabled. It is also the same with document library.
Related articles:
Sync with SharePoint tasks list from Project Professional
Sync with a SharePoint tasks list
Thank you for your kind understanding.
We look forward to your response. Thanks for your cooperation. Stay safe and healthy always.
Sincerely,
Zee | Microsoft Community Moderator