You've got a number of things on the car working against you: the all season tires, the Hawk HP+ pads, automatic trans, and a supercharger. Most of these can be fixed, but the auto and supercharger will always cause issue down the line. Be mindful at your next event of coolant temperatures, as the automatic will dump heat into the radiator and the blower will increase inlet air temps so that it makes the engine run hot as well. Normally I would give you a list of things to tackle, in stages, but the simple fact is - this is the wrong Mustang to use on track. You might realize this in a few more events, or maybe you won't...
As a new driver you likely won't tax the brakes too much, but eventually you will want better fluid (Motul RBF600 or better) and you need to
move away from Hawk HPS/HP+ pads, as they are not up to the task of sustained high brake temps. I know that the "normal Mustang guys" swear by them, but those people don't do track events... There's a reason why I have a dozen Hawk HP+ memes.
These pads will degrade RAPIDLY on track with a faster driver, which could be
you after a few more weekends with a good instructor. Your own increasing driving skills will push the car much further than you can imagine - you might drop 10 seconds a lap over the next 5-10 events - if you stick with this and have good instruction.
But before you get "mod crazy" and try to throw parts and money at this car to make it faster/fix issues, remember that the supercharger is always going to be your worst enemy. The thing is, most folks who find HPDE and get hooked rarely start with "the right car", or even a "remotely appropriate car". Don't take this as an attack on you or your mods, but that's just how this works. There are some charlatans on this very board who will tell you they have some magical tricks to make blower engines never overheat on track, but they don't have fast drivers on track with their wizardry, and they don't track events themselves. They just want your money.
No amount of radiators, intercoolers, heat exchangers, or other tricks will make a supercharged car with more than about 400 whp last a full 20 minute session on track, with a driver that is pushing the car. I've been working on cars and doing track events for over 30 years - there is no magic bullet here. It is just physics - there is only so much front area, only so much airflow available, to cool a heat intensive boosted engine. Boosted horsepower always comes with this nasty price - massive waste heat. I always have this talk with customers who bring us boosted Mustangs and want to do track events. I will no longer take people's money for intercoolers or radiators or other heat management work on these cars - because it is wasted work. 9 times out of 10 they don't listen, then when they frag a few motors they come back and admit "You were right all along... I never should have used this car on track". I don't like being right, especially after people spend tens of thousands of dollars trying to beat physics. GM and Ford have spent
billions trying to make GT500s, ZL1s, and ZR1s live at track events with boost. Its all a sham.
If you never buy a thing from my company, so be it - but I race what I sell, and I am not slow. I have more "proof" of my claims than these snake oil salesmen selling cure-alls and doo-dads.
Anyway, I'm glad you got to experience an HPDE and hope you get bit by the "track bug". Its a fun addiction and you will learn a LOT of driving skills you could never learn on video games or elsewhere.
Cheers,