@Jack Rabbit @SilverCX-5 @sm1ke @Mantra 7 @Paul_T @RedBaron thank you for the responses.
Had a call with the adjuster this morning. As you mentioned, they were able to assess the damage with the pictures instead of checking in person. They are probably going to replace the bumper.
I gave the adjuster my side of the story again and she said they will figure out who's at fault after listening to the other side as well. I don't see how I would be found at fault, but unfortunately I didn't have my dashcam installed so I can't provide any proof.
Turns out one of the Mazda dealerships has an agreement with my insurance company (not the one I go to, but same group) so I chose to get the repairs done there. Adjuster said I would receive a check and pay for the repairs with it. The shop will call me when they are ready to receive me.
I also received a call from Enterprise rental shortly after, I'll give them a call about the rental as soon as I know when I am dropping off the car.
About the diminished value claim, I am looking into it; but I assume it could only be done after I am not found at fault.