Target is so unreliable the past three years that I don't even bother with pre-orders.
I have a new system for finding stuff at Target, but it's far trickier than it used to be when their inventory management was the best in the business. circa 2022 and earlier. I used to post extensively about how to reliably find stuff at Target, but now they're so terrible if I told you all my system for finding exclusives there it has a high chance of making a difficult search even more difficult.
But I will share one general bit of advice. Target's web inventory system is awful beyond belief, but their in-store inventory system is just as accurate as it ever was, and really it's better than before their corporate system went to shit because they added a feature to their in-store inventory system that will search nearby stores and show Target employees when a nearby store has the item you're looking for in stock. And if you call them or ask employees in the store while you're there they're generally quite willing to look things up in that system.
Another tip is that their in-store kiosks access the same corporate database that Target.com does so they're just as terrible as the web site is. You'd think that the in-store kiosks would access the in-store system, but nope. Every time I've tried to use those kiosks they report the same thing the public web site does.