Avian has a couple:
Sinnoh- 'Asshole child rival who never lost until he got the clapping of a lifetime that Broke Him and caused a massive spiral.'
Galar- 'The spiral never stops! Burnt out gifted kid is now a chronically depressed macro cosmos admin taken advantage of by his bosses and the company'
Sinnoh2- 'So Darkest Day happened, time to deal with my problems, recapture my old team and get into a bare knuckle fight with Lord Regigigas again.

Stahl and Arryn share the galarian champion cup from 30-ish years ago, falling in love and getting married. Stahl became a corporate exec, was not caught tied to eternatus and unfortunately believes Rose Was Right and whether it be a few years or decades we just need to try again.

As for Arryn: There's the fact she's a faller from Hisui and then after marriage became a lawyer who just so happens to frequently be reigning tower tycoon at various battle facilities across the world, participate in underground battles, go on expeditions to find legendary pokemon and about to start her next snippet of her take in Paldea to figure out what's up with Koraidon and if she can go back.