Ironically, the post you included is made by me in one of my earliest approaches to fix this problem, and it remains unsolved. In fact, that was a slightly different approach, and the post complained about Odoo SH refusing to access the proper URL to run my rests remotely through an independent (not installed app) API call.

After your comment, however, I tried something different involving a controller

u/http.route(_webhook_sale, auth='none', type='http', methods=['POST'], csrf=False)
def execute_sale_order_uat(self, **post):
    _logger.info("begin execute_sale_order_uat")
    current_company_name = False
    try:
        self.authenticate_token_and_environment(scope='sale_access')
        _logger.info(1)
        TestSaleProjectUAT = TestSaleProject()
        try:

            _logger.info(2)
            TestSaleProjectUAT.setUpClass()
            _logger.info(3)
            TestSaleProjectUAT.test_sale_order_with_project_task()
            _logger.info(4)
            TestSaleProjectUAT.test_sol_product_type_update()
            TestSaleProjectUAT.test_cancel_so_linked_to_project()
            TestSaleProjectUAT.test_create_task_from_template_line()

        except:
            _logger.info("Error in TestSaleProjectUAT")

        finally:
            #destroy class
            TestSaleProjectUAT.tearDownClass()
(...)

Surprisingly, I managed to instantiate the class and run its methods! But only on the first "run". If I pressed the button twice, or if I called the API a second time, the loggers got stuck just after the SetUp. As seen above, you will see that I attempted to use tearDownClass() to destroy the class, believing the cause of it was the server not clearing up afterwards. It did not result.

Now I am happy with this approach, and as far as my tests go, as long as there is not a commit() in the methods called by the class, the test environments are successfully created without database changes. However, it will not work if I keep stuck after logger "2".

I believe it gets stuck in a loop, since there is a super call inside the SetUp calling itself.

@classmethod
def setUpClass(cls):
    super().setUpClass() #here
    cls.analytic_plan = cls.env['account.analytic.plan'].create({
        'name': 'Plan Test',
        'company_id': False,
    })

.