Also note the pull station mounted on the side of the panel

IMHO, No it does not. 72 does not say "Thou shalt not place a smoke detector in the FACP." But if you read through A-2-3 it is pretty clear on acceptable locations and placements.

BTW. That is a pretty funny picture.

I would like to know what that 12v- 4Ah? battery is for in the bottom of the cabinet.

That actually looks like a rate of rise detector from this angle...

I still don't think I'd mount in inside the panel...

Yes we have since fixed the smokehead issue that was in fact not mounted,just lying in there with just the wire to keep it in.
The Battery is for the dialer. this is in a high school.