1998-P Quarter Off Set Misalignment Or Something Else ?

I would say misaligned hubbing.

Not sure what to call it, but it is a nice example!

Not sure what it is, but it's pretty awesome! What does the reeded edge look like?

Per my understanding of misaligned die strikes, I think this is expected. The coin face area opposite the thick misaligned area does not strike correctly. This is because the force of both dies is required to strike the coin features. That missed area on the reverse corresponds directly to where the obverse did not strike properly due to insufficient pressure.

I guess that means the reverse was the hammer? I don't know much about misaligned anvil dies, if that was even the case here. What do the reeds look like? Also, is the coin properly circular? It almost looks broadstruck in that area, although that could just be an optical illusion to my brain because the coin face looks abnormal.

EV ,here're some pictures of the rim a the location of the event and the last one on the rim at the opposite place of the event

Yikes. Is that thick rim section on the reverse a bit cupped? Because that smooth edge with barely any reeds is more reminiscent of a partial collar.

https://www.error-ref.com/?s=Partial+collar

Yes, misaligned die with partial collar. I just put two such critters up on ebay tonight but neither are really comparable or you could learn what it would sell for.