I think this could be explained by accidentally swiping a tiny bit to the right.
Swiping right will take you to the camera view, so even swiping a few pixels to the right and then releasing will briefly activate the camera.
Settings -> Instagram -> "Allow Instagram to access" -> Camera
The app will still work, it will just prompt you for the permission when going into the camera view.
We still want to know why this step was necessary. After all, this disables a useful feature for the sake of preventing… what exactly?
And yep, it was 100% triggered by a slight movement to the right while holding finger down anywhere on the left edge in the main feed. And it happens even if you just move it by a few pixels, to the point where someone else looking at the screen might not notice.
As someone else has already pointed out, OP can just revoke camera permissions from instagram in the phone settings. The app will still fully work, and will just ask for camera permissions if you attempt to use any features that actually require camera access.
P.S. I feel it is rather difficult to trigger accidentally though, and I am saying it as someone with large hands/fingers. It happened to me before a couple of times over the years, but I've noticed instantly, and not because of the camera LED lighting up. I've noticed because the entire rest of the UI becomes unresponsive (e.g., scrolling up/down doesn't work) until you release the "swipe right" gesture hold, which makes perfect sense. So you cannot really stay in that weird state, unless you are committed to holding your finger on the screen in that spot without moving or releasing it.
In contrast, our tests today show that swiping right to camera mode does cause the indicator to turn on briefly (as expected), but it goes away almost immediately when returning to the normal browse mode. Not the same.
It was very plausible in the past, but Android and iOS have regularly been ramping up privacy. The latest for Android seems to be that only one app can run a camera at any one time, and a green icon appears at the top of the screen when camera/mic permissions are active.
People always seem to think I'm paranoid about this, but I've been asked by so many potential clients to actually code this in their "free" apps.
As for Meta, there are a lot of things that make me highly suspicious. While we have screenshots of FB and WhatsApp being dodgy (e.g. camera running below the UI, some experiments on linking WhatsApp to FB ads), there's never been any damning proof. So it's best to assume incompetence and not malice.
I'm sure it's only a matter of time before they ruin it, too, though.