Thank you all for the responses! I am leaning towards replacing the door now. I will include some photos below.
To answer some questions:
1) No this is definitely not the first maintenance request in 5 years. Each year when the lease is renewed (and the rent increases) there is something that goes wrong that has to be replaced or plumbing that has to be unclogged. There are also other repairs at random times.
2) The $150 only replaces the window. The crack would still be in the door, and any caulk or repairs wouldn't be painted. I do not think this is a very good price for how poorly I think it will look afterwards.
3) I think part of my post was grieving against the PM company as well. They have had a history of fixing stuff (>$300) without my knowledge (contract says anything over $200 they would notify me), ever since they brought their repairs in house and no longer get bids from different service companies. It feels they are partially encouraging repairs, but I don't have any evidence of that.
Here are the photos of the door crack and the window crack. They put a piece of tape over the window. I believe a BB or something is what caused the hole and caused the window to crack. I can include before pictures if anyone wants to see those, but they would be identical, just a different piece of tape.
Door Crack