For video, sensor size affects both dynamic range and noise, but there is a third factor: pixel binning and oversampling. The DJI Mini 3 Pro shoots 4K video from a 48MP sensor by binning four pixels into one. This pixel binning reduces noise compared to reading each pixel individually.
The result is that Mini 3 Pro 4K video has less noise than you would expect from a 1/1.3-inch sensor at equivalent ISO. Similarly, the 4/3-inch sensors in the Mavic 3 Pro oversample their resolution for video, further reducing noise.
Sensor size sets the ceiling on quality; the processing done to that sensor data determines how close the final output gets to that ceiling. Modern image processing has narrowed the gap somewhat, but physics still wins -- the larger sensor always has a head start.