This is easy to respondA rival should be something more than a trainer that you battle multiple times.
Should be someone who you aspire to defeat, your antithesis, the one who have a different "savoir faire". Not only in battles but in all aspects, and specially not someone who you see once in a year
That's why Paul was so good.
Calling Bea a rival because you could not beat here is insulting, but this is Pokémon Journeys...
And let's not talk about megaevolution. What is the reasoning behind that? He just wants to have a Mega Lucario?
"It insists upon itself Lois"
Rival definition: "a person or thing competing with another for the same objective or for superiority in the same field of activity"
Basically many of the trainers Ash battles throughout the series are his rivals. Everyone participating in all leagues, tournaments, competitions, etc...
There can be a difference in rivalries, intensity, superiority.
We could say Ash's rivalry with with Gary, Paul and Alain to be superior to his rivalry with Morrison and Cameron.
But still, they are all rivals. It's the definition that matters.