I've made this work, but it's probably not supported as it uses a private API call /private/investmentTemplateCopier with this POST payload
{
"templateId": "5000004",
"name": "CCCCC",
"objectAlias": "projects",
"_objectAttributes":{},
"scheduleStart": "2025-06-12T15:39:00",
"scheduleFinish": "2025-06-12T15:39:00",
"code":"ccccc"
}
The templateId is the OOTB Major Project Template. CCCCC and ccccc are the name and ID for the newly created project. It copied the Team and Tasks across, but it's your choice of whether you want to go down this route.
Good luck,
Paul