Triggering based on the webcam is very smart.
I can think of at least 5 different companies that have tried to launch similar products, including a couple local startups. Most of them had some sort of manual control which everyone gets tired of after a couple days. The few people I saw try to use the manual lights would forget to turn it off, which turned it into a false alarm system, which quickly taught everyone to ignore it and peek their head in anyway because it was on so frequently that everyone knew it had no actual correlation with the person being in a meeting.
I use a StreamDeck with MuteDeck (which basically provides a consistent tooling for the buttons regardless of Teams/Zoom/Meet).
MuteDeck can also integrate with hardware tools, specifically the Plenom Busylight (https://busylight.com/), which actually got a lot more reasonable price-wise from my memory ($50). They have a couple of different types of light mount.
But for now I'm fine - I work from home, desk is in the middle of the room facing the door (so camera is aimed at me and far wall). If my partner walks in, she can see the camera status on my Insta 360 camera on my monitor which has a green light visible from any direction if the webcam is live.