I'm fairly confident that metal rapping sound is not from the engine itself. That would be an extremely alarming sound to come from the engine core.
Almost certainly from a belt-driven accessory or pulley.

...unless your valve spring broke...
I notice you have 2013 FRS.
A broken valve spring or non-operational valve would explain pretty much all of these symptoms.
Wouldn't quite explain the whole 15sec thing though.

At this point, I suppose it's pointing more towards an injector issue.
I guess make sure there isn't an injector plug loose.

Again, not trying to be vague, but these audio/video diagnoses suck with the poor audio quality. Very hard to determine exactly where the noise is coming from. Like higher, lower, left, right, etc.

Why don't you use a stethoscope or long screwdriver to determine more specifically where the noise is coming from

Just watched the 2nd video.
You definitely got at least 2 issues going on there.

Motor is missing pretty bad, and then there's that metal sound.
Metal rapping sound is far too slow to be from the engine internals.

Almost sounds like you have a nasty exhaust leak as well.

Why are you putting your hand down into the bottom of the engine bay in the video?

I’m not sure what the metal rapping noise is from as it comes on at the same time it begins to misfire. And I cropped the video, I was unplugging the coil pack to see if it it had an effect or not
-Sheesh now an exhaust leak, I’ll have to check that out. What noise is the exhaust leak making?

Exhaust leak is a flange leaking a bit of air. It will create like a raspy, muddy, air puffing noise. You mentioned aftermarket exhaust, you might want to recheck your flanges for leaks.

Engine seems to start at like ~1800rpm.
The exhaust-leak-like noise is most prominent in the beginning. It stops sharply at 8 seconds in the 2nd vid.

At that point, the engine slows down (maybe 1000rpm), the exhaust leak noise goes away, and the metal rapping starts. Although I'm 50-50 if I can very faintly hear the metal rapping (at higher speed) starting at like ~6 seconds. Could just be my imagination.

At 10 seconds, motor seems to speed up slightly (maybe 1250 rpm). No real other changes.

Stays mostly the same until 24 seconds when you seem to unplug the coil.
Motor slows down again (like 800rpm) and seems to miss more. Or motor sounds slower due to cylinder missing.

I guess the "exhaust leak" sound could simply be how your aftermarket exhaust normally sounds, but I wouldn't expect the microphone to pick up your exhaust note (from the tailpipe) so prominently while recording from inside the engine bay.