I just woke up and went " okay what's the history of Poké Balls and how old his Drayden", so here we go! Please note that a lot of this is based on my own headcanons for the specific dates when certain events happen.
Let's get the general basics down. The invention of Poké Balls as we know it came from Johto with the use of apricorns, which is shown in pla with some extra ingredients.
The modern PokeBall, the one that trainers use in modern day, was invented in 1925( this isn't a headcanon, it's there in Bulbapedia). The modern PokeBall and the ones made in pla are not the same. I mean, clearly, but it's best to make this distinction now.
Now that we got that out of the way, let's move into Drayden. He had mentioned during his childhood ( key word: childhood) pokeballs didn't exist during. Now this kinda supports my theory that different regions were introduced to pokeballs at a different time. We know that Kanto and Johto had already got it locked down due to their natural access to apricorns to make the pla version of PokeBalls, and Hisui, by the start of PLA, have only recently started to use it more. We don't know much about Hoenn's history, sadly. Unova, as far as we know, didn't have access to apricorns back then. So maybe they were introduced to pla pokeballs later.
This might apply to both versions of the pokeballs, cause when you really think about it, Kanto kinda holds the monopoly on that, next to Hoenn with Devon Corp. 1925 , when the modern PokeBall was created, could have capped the fastest production and selling of PokeBalls ever. I say this because, in another hc, pokeballs would have had to exist before 1970, since that's when Opal and Mustard battled. And with Silph Co, I'm honestly inclined to believe that.
And this is where the math comes in! Some hc( and non hc) dates you need to know:
PLA takes place from 1868-1872. The pla pokeball was most likely invented before then, in Johto ( maybe a different variant due to different resources in Johto but I digress).
The modern PokeBall was invented in 1925 ( not hc)
The conversation between Iris and Drayden when he mentions pokeballs, at most, happens right after bw. This is because Iris is already champion here in that convo. So, nearing the end of 2012, since that's what I hc that's when bw takes place, or at least 2013. I'm not sure if these dates will be brought up but juuuuust in case it does, here.
The time between the beginning of pla and the time of the creation of the modern PokeBall is 57 years. Given how PLA pokeballs might have been created before then, we'll say 57+( not a big plus. Laventon did say that pokeballs are a recent creation in pla). If Drayden is purely talking about the pla pokeball ( as by 1925 and onward the modern PokeBall would be mass produced and sold everywhere), then it would probably be somewhere between those years where he was born. I don't think Drayden is that old, so I'm not gonna say he was born around pla. No. I am going to say he could have been born around the early 1900s, which, and I kid you not, make him about 112 years old by 2012( hey look 2012 did come in for something!). What. Opal is 88 by 2020, and Drayden over here being 112, the buffest man alive, in 2012. What the hell. I guess this kinda feeds the headcanon that Drayden, at the least, has some longevity to him. Like damn.
No could I be wrong about all of this? Absolutely! I didn't mention Kalos' PokeBall factory, or the fact that the Isle of Armor had a natural supply of apricorns. So what about them? How do they fit here? And honestly I don't know. Even with the information given to us plainly, there're still so many variables to take into account that can flip this entire theory on its head. But I guess that's part of the fun haha. I hope I was able to get my ideas across well, and sorry if it turned out to be a complete mess. But I hope you guys had a good read as much as I enjoyed writing it!