In 1820 Hans Christian Ørsted noticed that an electric current could affect a magnetic compass. By 1862 James Clerk Maxwell had developed Maxwell's Equations for electromagnetic waves. People thought of the medium for electromagnetic waves as the lumiferious ether. However, the 1887 Michelson Morley experiment contradicted the ether theory. Maxwell died in 1879. It was not until 1897 that J. J. Thomson proposed that there were electrons about 1000 times smaller than atoms. By the time electrons were beginning to be understood the idea of any medium for light was associated with the discredited ether theory.
To me it seems odd that although electricity is moving electrons and magnetism comes from electrons going in circles, people don't think of electrons as the medium for electromagnetic waves.
A sound wave is where the whole atom moves back and forth. In an electromagnetic wave the main motion is just in the electrons. In heat the atoms are moving fast enough to make electromagnetic waves.
I suspect that if electrons had been discovered before Maxwell started working on the problem that he would have understood that electrons were the medium and today we would call these waves "electron waves".