The Pokedex
The pride and joy of Professor Oak and the mark of prestige among trainers. The pokedex is a digital multitool, serving as an ID, research device, digital encyclopedia, and many other uses. In this new era where the national infrastructure broke down, this has become a frighteningly powerful tool from the sheer information it provides, on top of being a mark for fellow trainers sponsored by oak to find each other, and even talk to each other if close enough. And if anyone thinks of acquiring one for themselves, these pokedexes are registered directly to the trainer it was given to, and will refuse to function for anyone else, so mor most anyone, the only way is to basically find one unregistered, or be given one by Oak himself.
The Pokedex is said to be linked to a special database to facilitate the Dex Holders role as researchers, gathering Pokémon to help further study and giving tools for the Dex Holders themselves to gather data directly. A fact, which when paired with Professor Oak being the foremost expert in all things Pokémon, means that short of products of recent science, there is very little knowledge involving Pokémon a dex holder isn't in relatively easy access of. It's so advanced, with enough data, a dex holder could acquire a loose estimate on the strength of a Pokémon not their own from the device, especially powerful even if there is limited knowledge on it's function.
The pokedex is also a tool of identification and communication, between it's ability to detect other pokedexes being nearby, and even has limited ability to communicate longer distances, although mostly through recordings. At relatively close distances, the Dexes can function sort of like radios, though the exact method is unknown. This encourages networking between them and enables a degree of coordination, even at a distance that would normally not be feasible, something that will only be emphasized by the type of people whom received it, people whom caught the eye of Professor Oak himself.
There is a saying that Knowledge is Power. And, well, the Pokedex is as close as it gets to absolute knowledge about Pokémon. Knowledge on their own team and conditions come easy with it's analysis abilities, they can pull up information on nearly any pokemon they encounter, and with a bit of effort, get info on the specific pokemon. They can connect and communicate with possible allies with comparative ease, and given their own skills, assuredly exceptional enough to get Oak's attention in the first place, will only serve to amplify the advantage.
A/N: Yes, I am running with the pokedex being ridiculous, why? Blame Celibi giving Oak an idea of the crisis way before it happened, influencing design to be warring states proof, and also in part the canon features becoming way more valuable thanks to infrastructure breakdown.
Honestly, I have a feeling, there is a chance activating the Lab might have boni besides research, given there is probably a network of pokedexes out in the wild, between canon features and the whole blend of all timelines and Prof Oak's time adventures which inspired said pokedex. That thing in the manga is basically a multitool, and the anime has one version being able to analyze and extrapolate the abilities and strength of Pokémon without capturing it. Only feature mentioned here without much direct basis, is the communication one, and I extrapolated it as a possible feature between features like the dex detector, recording ability, and other points.