[iOS] Support badge background/text color

[ardasatata]

Summary

tabBarBadgeBackgroundColor / tabBarBadgeTextColor (badgeBackgroundColor / badgeTextColor on the TabView routes) are Android-only today (#473). On iOS the badge always renders in the system red. Would you be open to iOS support, and if so, what API shape would you prefer?

Our use case

We show a small dot badge on one tab (a "new item" indicator). The system red is visually too strong for our design, so we'd like to use a softer color. Badge size is a lesser concern, since the iOS badge size is system defined.

Ours	Original size

What I found (react-native-bottom-tabs 1.4.0, iOS 26.5 simulator)

The JS side already forwards the per-tab colors to the native component, but the iOS side doesn't read them. I tried to wire them up with public UIKit APIs only:

• Per-tab UITabBarItem.badgeColor and setBadgeTextAttributes(_:for:): no effect, the badge stays system red.
• Per-tab UITabBarItem.standardAppearance with a UITabBarItemAppearance carrying badgeBackgroundColor: no effect.
• Bar-level UITabBarItemAppearance.badgeBackgroundColor inside configureStandardAppearance: works, but it applies to every tab's badge, so a per-tab color isn't possible this way.

So with public API, iOS 26 seems to only allow one badge color for the whole tab bar. I did not test iOS 18 or earlier.

Our workaround

For now we apply the color from a small local native module, by pinning backgroundColor on the private _UIBarBadgeView inside the UITabBar with KVO (UIKit resets it on relayout and while dragging the iOS 26 selection lens). It works, but I wouldn't propose that for the library since it relies on a private class.

Question

Would a bar-level option be acceptable (for example a single badge color for the tab bar on iOS, alongside the existing per-tab Android props), or is per-tab iOS support something you'd want to solve differently? I'm happy to send a PR for whichever direction you prefer.