I was driving my 04 6MT coupe a little harder than I usually do earlier tonight and I accidentally shifted into the wrong gear (newbie mistake I know this is my first stick car) and I redlined for a moment. I immediately heard I was redlining so I dropped the car into neutral and applied the brakes to slow the car and engine speed down. Ever since then I've had the brake and battery light on in the dash and the power steering was gone. I restarted the car once on my drive back home, but as for right now the cars parked outside. Did the engine go into limp mode to protect the engine from further damage (considering it was literally only a moment I do not believe I caused permanent damage but I am also internally freaking out since it was a pure accident due to my own incompetence and its my first car) ? Or is this something more and I messed up.

I suspect two tings.

Most likely, its your alternator. I've seen a few go out this way. If you can take it out yourself, you can take it to be rebuilt and that will likely last the longest. You can also buy from your local auto parts store, but those tend to be so-so and don't last very long.
I would also check your battery ground, it could be loose. While at it, check all your grounds as well. That is my next suspicion.
So actually, check ground first since it's the cheapest thing to do.
Also, check all your fuses to see if any popped.

Open the hood and check the belts.

Good point, particularly the alternator and the tensioner, the tensioner could have gotten loose. I'm still betting alternator.

Either way...time to crack that hood open.

Sounds like you chopped the belt, it's probably laying in the bottom of the engine bay on the plastic shroud.

Nothing else is going to kill your power steering (driven by belt) and your alternator (driven by belt).

Possibly the idler or tensioner pulley gave up the ghost. Should be pretty obvious what the problem is.

OP, post whatever you find is the answer, always helps the rest of us.