The "returning (Pokemon) to (name of the trainer)" message no longer exists in Scarlet and Violet. Even if all the trainer details match, it still doesn't display that message when trading someone's pokemon back to them.
The reason that Pokémon traded in Scarlet and Violet refuse to obey, even if they match the original trainer, is because Scarlet and Violet have an additional preventative measure. They track the "met level" for the original trainer, but they also track the level that the "previous non-original trainer" had that pokemon as.
This means that if you catch a Pokemon at level 5, and level it up yourself, it will obey you even if it surpasses the number of badges you have, but if you catch a Pokemon at level 5, trade it to your friend, and have them level it up instead, when traded back to you it will disobey until you have the required number of badges.
This feature is unfortunately triggered even if you overlevel a pokemon yourself, trade it to someone, and immediately trade back. There is no way around this feature, you will not be able to trade people high level pokemon that obey them if they do not have the required badges, even if all the trainer details match.