There are perceptual hashing algorithms for images/video/audio (dsp and ML based) that could work for that.

Given that the TV is trying to match one digital frame against another digital frame, you could probably get decent results even with something super naive like downsampling to a very low resolution, quantizing the color palette, then looking for a pixel for pixel match.

All this could be done long before any sort of TV-specific image processing, so the only source of "noise" I can think of would be from the various encodings offered by the streaming service (e.g. different resolutions and bitrates). With the right choice of downsample resolution and color quantization I have to imagine you could get acceptable results.