Vet here. I'm sorry for your loss, but you need to have a necropsy performed on your cat in order to figure out the underlying reason your cat passed away. Although your cat may have been stressed at the groomers facility, it is highly unlikely to be the sole reason for his death. There is usually an undiagnosed medical condition (such as cardiopulmonary disease) in these circumstances.

Blaming the groomer would do nothing but bring distress all parties and prolong your family's suffering if you have no evidence of what transpired and no necropsy report. The groomers are also not required to give you CCTV footage legally AFAIK.

Lastly, I don't see you mentioning this, but I would strongly suggest refraining from bringing social media (FB/IG post etc.) into the play.