I’m glad you had fun. You had a great instructor. He really wanted to make sure that you got a real sense of what it is like on the track. You will find out that as you gain experience and start moving up groups every driver is always pushing their car. It actually makes things safer because you can anticipate when a car is going to close on you.
If I see a Porsche GT3 in my rear view I know that he will be on top of me in a second. And I will start positioning my car on the track to allow him as uninterrupted pass as I can manage.
If I see a Miata, I know that he is faster in the corners and give him the point bye in turns 5 or 6.
If there is a comparable car such as a S2000 or 3 series BMW, I will wait for the most awkward off line pass and see how good he is.
I watched your video and you were not experiencing limp home mode. That was fuel starvation. That is the reason I bring gas cans so I can top off my gas to the point of having fuel in the filler neck. Normal gas pumps will not allow you to fill your tank really to the top.
Even with my method, I would start getting fuel starvation out of turn 2 after 20 minutes.