You're around my age. Funny, because I always assume people our age who were never fans but who try to get into the series now would never succeed in doing so. I feel that the subgroup of people our age who enjoy the series do so because of a very specific set of circumstances that began with the games release.
The series was touted as a Disney/FF collaboration and that shit was SO weird at the time that us kids were curious and excited. The idea appealed to a variety of Disney and Final Fantasy fans and we picked it up.
Because the first game's story leads directly into the second game (technically into KH:CoM first tho) , and the second game EXPLODES into the rest of the games by opening a myriad of possibilities for the future of the lore, it had us absolutely hooked by then, almost as if we had no choice. KH2 Era is when the series becomes its phenomenon.
The series then pulls you forward because each game answers some mysteries, then opens others, and you feel you MUST continue. At this point you're trapped. It's maddening, it's beautiful, it's the best experience you could ask for. The most important factor here tho imo is TIME between each game. The fact that we had to wait some years between each game to have mysteries explained made them unbelievably exciting. What did the secret movie mean? What is the intention behind this seemingly unimportant line of dialogue that's revealed years later? We speculated online, we created theories, the amount of time between each ganme let these feelings brew into something strong and catapulted us ever forward.
NOWADAYS: I'd be very surprised if people our age could get past step 1. Disney culture has permeated everything to the point that KH would be seen as lame or white noise among what's available now. To a lot of people KH couldn't be seen as special from the get-go, and I find that sad. But say a person does get thru step 1. By the time you get to step 3, you have the entire series in front of you and to binge essentially. The sense of waiting, of the mysteries brewing for years, an element I feel was crucial to the fandom, is lost on a new player that can play each game immediately after the next. That special something is removed. Compare it to watching a really damn good show on TV for the first time versus binging it for the first time on Netflix. I think the latter makes it less special because you don't have any time to really be excited between each episode release.
But you seem tremendously open-minded and that's fantastic. You seem like a kid at heart and that's EXACTLY what it would take to be an old-aged but NEW fan of the series. Please keep up that spirit and I know you can take the same journey as we all did back in the early 2000s. I've got 2 suggestions if you want to replicate the experience: play the games in the order they were released. It sounds like you're doing this already (as story chronologically, KHBBS takes place before 1). Playing by year release is vital to the way the game developers chose to release and reveal information throughout the franchise, and the the way mysteries are discovered or solved is way better this way. The other suggestion is to take maybe a week or two between playing each game to duplicate that feeling of waiting and letting yourself soak up that wonderful KH mystery juice. Let things marinate a little.
Anyway, sorry for text dump, but I think it's very cool that there's new fans forming out there. Most of my friends couldn't get into the series so it made me sad, and made me think about why. Most importantly, just do what you want and have fun!