I found the source of my problem. Because iOS 26 puts more space between navigation bar and toolbar items, I had to rework the way I'm adding items to navigation bars and toolbars to preserve the original spacing that my app is designed for. And my new code was adding some empty toolbar items every time it ran. So when I moved my app to the background, or resized its window, empty toolbar items were added that made the visible items no longer fit.
I still don't know how to prevent toolbar items from going into an overflow menu, or how to make the overflow menu actually show the hidden items instead of just doing nothing when clicked. But by stopping the addition of extra toolbar items, the real items really do fit and remain visible as before.
Topic:
UI Frameworks
SubTopic:
UIKit