No, there is no way to prevent sites from uploading the info besides just not providing it in the first place.
And because of how programming languages work, there’s no way for the browser to identify that data being uploaded “is” anything specific, especially when there’s things like encryption, obfuscation or just re-arranging the data itself into larger collections of data.
When you say “app” do you mean something that will let you view remotely through a residential NAT connection with no port forwarding or hole punching? Because 99.9% of those options are inherently not private.
If you only need the camera itself to have a local feed i.e. you already have some kind of VPN/tunnel/etc. into your home network, then something like a cheap Amcrest works fine and does not require Internet access for the camera itself.