First off, to understand my choices, a bit of background. I like to capture pokemon using the least effective balls possible, for bragging rights. When I battle someone, I want them to know that I consistently capture pokemon the hard way whenever I send something out. In 7th Gen, for example, that means I use a Beast Ball on everything but Ultra Beasts, and on Ultra Beasts, what I always use are Premier Balls since they take the longest to obtain significant numbers of. You may think I'm weird, and you are welcome to that opinion, but I like to do things in my own way.
As for the topic of this thread, for me, it's Shroomish/Breloom. Not for any region-specific reason, but because Breloom is an ideal pokemon for capturing others. It has access to Spore, False Swipe, and Swords Dance, and can know Flash if from Gen 6 or earlier (allowing it to avoid hits while maintaining accuracy change even if it faints). Not only that, but it is the only pokemon with any sleep move at all that has access to the Poison Heal ability. While the amount healed is superior to Leftovers, there is another, better reason to use Poison Heal over Leftovers, for when poisoned, the Breloom can't be paralyzed, burned, frozen, or put to sleep. It's really handy.
Also, I hope Galar has Durant, for a similar reason. In this case, a Durant with its Hidden Ability of Truant is an amazing tool for capturing pokemon with low catch rates. Just max out its speed and level, send it out early in the battle, and have it use Entrainment. Suddenly, instead of getting any sort of bonus from its actual ability, your target can only act every other turn, potentially doubling the amount of time you have to catch it. More than doubling it, actually, in some cases, since if it wakes up on a turn where it can't move, it can potentially be put to sleep again without acting.
Lastly, I will be somewhat irritated if both Grumpig AND Slowbro are not in the Galar Dex. Same reason as the last two, but as much more of a niche capture tool. Grumpig + Own Tempo + Skill Swap is a great way to catch pokemon knowing Thrash, Petal Dance, and Outrage. By making them unable to confuse themselves, it becomes a simple matter to capture almost every time. That's the only (likely) way it's even possible to catch a Guzzlord with anything but a Beast or Master Ball in 7th Gen, after all.