I would start here, to see which approach works best for your needs: [here]. Both the "Legacy" and "Cloud" based options allow you to use a local physical device or emulator you manage - or 3rd party services in the case of the Cloud option. Appium has some options to run the Safari driver only, so I would also suggest reading their GitHub documentation [here].
Should have mentioned that I use BitBar. I have a keywordtest that's running (in parallel) in BitBar on different browsers. I want to run similar tests in BitBar Mobile Cloud, but when I select device to run on (i. e Apple iPhone 11 Pro) TestComplete needs to know the application to test:
Here I'm not able to tell TC that I'm not testing an MobileApp, I want to use Safari. Forgive me if my question is stupid 😞