Radio won’t turn on display works, speakers work

The "head" unit for the display of the audio system is not the same as the audio control module (ACM), which is behind the dash in the same area. As such, diagnostic testing is possible for the ACM -- using a Ford IDS diagnostic tool or equivalent. Not sure about the correlation between the engine work and the climate control / audio unit concerns, but I would definitely have the repair shop recheck their work in the event something was affected.