The basic principle (left toe, right toe, left heel, right heel, keeping the heels and knees together) used in playing scales comes from the French legato organ school which was basically invented by the Belgian organist Jacques-Nicolas Lemmens in the middle of the 19th century.
However, unlike with manual scales where there is a certain uniformity in fingering, pedaling was never uniform. The main principles are there but certain authors (Dupre, Gleason, Davis, Ritchie/Stauffer and others) can differ slightly from one another with their scale pedalings.
In this video I play 5 pitches (C, D, E, F and G) with the left foot only because some people would feel it very awkward to play with the right foot on the D and F. Other authors might be a little more strict with their approach.
Of course, if we would be dealing with early organ technique, then the proper way to play the scale would be with alternate toe pedaling - left, right, left, right etc. Importantly, there is no foot crossing here - you have to move both feet together as a unit.
Two feet are like two fingers of an extra hand in early music (and to a certain extent for the Romantic music, too).
[Thanks to Andreas for inspiration]