For iOS, I guess if you just update the bottom navbar (if you're using it) and use the fancy new glass back buttons that should be enough to keep them looking updated without breaking the UI in major ways.
For macOS maybe keep original toolbars (instead of the new floating-inside-a-floating-box ones) or make a custom UIView that emulates what's currently on Sequoia. Same for sidebars. Those two alone would IMO make it better than the built in apps on Tahoe.
And a design classic, an inner rounded rectangle should have a smaller corner radius (less rounding) than the outer one AND the inner rectangle should maintain significant margin between itself and the outer rectangle's borders. This is why the new Finder sidebar looks so tacky, they got the first part (corner radiuses) right but since the two elements are so close to each other there's still a visual clash between them. How to avoid it? Use a flat sidebar with a border only on the right.
For macOS maybe keep original toolbars (instead of the new floating-inside-a-floating-box ones) or make a custom UIView that emulates what's currently on Sequoia. Same for sidebars. Those two alone would IMO make it better than the built in apps on Tahoe.
And a design classic, an inner rounded rectangle should have a smaller corner radius (less rounding) than the outer one AND the inner rectangle should maintain significant margin between itself and the outer rectangle's borders. This is why the new Finder sidebar looks so tacky, they got the first part (corner radiuses) right but since the two elements are so close to each other there's still a visual clash between them. How to avoid it? Use a flat sidebar with a border only on the right.