Why does my iPhone 15ProMax camera every now and then move to video mode instead of photo?

It’s easy to accidentally lightly brush the screen for the input to be interpreted as a mode change. There is no getting around that I’m afraid. You can use the Preserve Settings feature to make Photo mode the default mode. That way every time you turn the camera on, Camera app will automatically set your preferred camera settings for you.

Please follow this path,

iPhone > Settings > Camera > Preserve Settings > set the camera up the way you want and then turn on the features to make it the default.

Yes it can be annoying. Personally I'd like to see a real physical shutter button to press than a touch point on the screen. It's the main reason why I still prefer using a dedicated camera with a viewfinder over phones and tablets.

You can leave feedback to Apple if you wish: Product Feedback - Apple

You’re welcome and I hope you have a great day!