Home door "open/close sensor" without installation
If you can't modify the "B side" at all, then you have to rely on detecting something that's already there.


An optical sensor can detect the painted surface, but can easily be fooled by something passing by the edge of the open door, or by light shining on it.
A metal detector might be more reliable, and have fewer false positives when open. This will be more complicated to implement if the jamb plate is non-ferrous.
A simple mechanical switch might be your best bet. This type could be located either on the latch side or the hinge side of the door.