By what approximate angular measurement is Polaris currently offset from the true north celestial pole?
About 0.7 degrees.
Although Polaris is commonly called the North Star because it is extremely close to the north celestial pole, it is not perfectly aligned with the exact axis projection. Currently, the measurable offset is slight, amounting to approximately 0.7 degrees away from the true pole. This small angular distance is crucial because it means Polaris does trace a very minor circular path over a full 24-hour period. For perspective, this minuscule circuit is only slightly wider than the diameter of the full moon, which itself spans about half a degree across the sky. This tiny deviation requires specialized observation techniques to confirm, as the naked eye perceives Polaris as stationary.

#Videos
Why is the North Star Always in the Same Place? - YouTube
Why Do Stars Draw Circles Around Polaris? - YouTube