I found it interesting that most of digital images taken by camera consist of color signals that are not measured by the sensor but actually interpolated. How do the camera designers ensure that these interpolated values preserve the actual visuals of a scene, even though there are multiple filters and camera processing steps happen before the digital display that could further reduce the original quality of the image?

This doesn't fully answer your question, but (not too surprisingly) it seems the R, G, and B values aren't fully independent. Someone can use the other colors to get information about the missing one, a concept explored in depth here: https://www.microsoft.com/en-us/research/publication/high-quality-linear-interpolation-for-demosaicing-of-bayer-patterned-color-images/

This website describes what can happen when the frequency content of the image is too high such that we can no longer assume that a red, green, and blue pixel are in the "same location." https://www.japanistry.com/moire-false-colour-anti-aliasing-filters/