based off the endpoint you are utilizing here it looks like you are trying to add a task to a specific project. based off the docs you should be using PUT, so just change:
root@b5dd7b*******:/# curl -X POST http://synology.***************.com:3456/api/v1/projects/1/tasks \
-H "Authorization: Bearer tk_75454cb33****************" \
-H "Content-Type: application/json" \
-d '{
"title": "Neue Aufgabe",
"description": "Beschreibung der neuen Aufgabe",
}'
to
root@b5dd7b*******:/# curl -X PUT http://synology.***************.com:3456/api/v1/projects/1/tasks \
-H "Authorization: Bearer tk_75454cb33****************" \
-H "Content-Type: application/json" \
-d '{
"title": "Neue Aufgabe",
"description": "Beschreibung der neuen Aufgabe",
}'
and this should work