def METHOD_NAME(project_id: int, project: ProjectIn,
                   Authorize: AuthJWT = Depends(check_auth)):
    """
    Update a project detail by project_id.
    Args:
        project_id (int): ID of the project.
        project (Project): Updated project data.
    Returns:
        dict: Dictionary containing the updated project details.
    Raises:
        HTTPException (status_code=404): If the project with the specified ID is not found.
        HTTPException (status_code=404): If the organization with the specified ID is not found.
    """
    db_project = db.session.query(Project).get(project_id)
    if not db_project:
        raise HTTPException(status_code=404, detail="Project not found")
    if project.organisation_id:
        organisation = db.session.query(Organisation).get(project.organisation_id)
        if not organisation:
            raise HTTPException(status_code=404, detail="Organisation not found")
        db_project.organisation_id = organisation.id
    db_project.name = project.name
    db_project.description = project.description
    db.session.add(db_project)
    db.session.commit()
    return db_project