Accessory downloading firmware message
It’s been a while since this question has been posted, but I recently encountered the problem and I may have discovered a solution for some of you.
I have been doing the same by using my iPhone connected to an HDMI accessory cable in order to watch videos on my TV. It was working fine , but I began having problems with the accessory firmware downloading message appearing.
Turns out it was related to updates downloading on my Samsung smart tv, which I had set to update automatically. Removing the automatic setting solved my issue. Hope this helps.
iPhone 11 Pro Max, iOS 18