Does the FAA require a specific grade of supplemental oxygen for part 91 operations?
Regulations don't usually include detailed technical requirements or specifications, but AC61-107B - Aircraft Operations at Altitudes Above 25,000 Feet Mean Sea Level or Mach Numbers Greater Than .75 / with Change 1 says (p. 33, emphasis in the original):

Only oxygen that meets or exceeds the Society of Automotive Engineers
(SAE) International Aerospace Standard AS8010 (as revised), Aviator’s
Breathing Oxygen Purity Standard, should be used.