You gave 0 sources of tournaments, not just competitions, were done of higher ranking nobles.
It doesn't have to be part of a regular tournament, it could be its one separate competition, but if you want to split hairs fine I'll find more sources.
Obviously if the nobles competed with commoners they were not high ranking nobles as no lord or duke would compete with a bunch of commoners.
"The local and regional nobles were often present at the competitions
and sometimes took part in the shooting. Often the local noble would
lead off the competition by shooting first. "
Judging by the terms "local and regional" I would assume this referes to the local knight and regional barons, viscounts ect. The rules of who a noble could associate with were not as cut and dry as Battle Master would have you believe.
