Remove unused UIManager binding from React private interface (#58399)

Summary:

After Paper was cleaned up from React in react/react#36285 this property is no longer used in React and can be removed from the interface.

Changelog: [internal]

Reviewed By: cortinico

Differential Revision: D119166138

Author: rubennorte

packages/react-native/src/react-private-interface.js

@@ -42,7 +42,6 @@ import typeof {
   create as createAttributePayload,
   diff as diffAttributePayloads,
 } from '../Libraries/ReactNative/ReactFabricPublicInstance/ReactNativeAttributePayload';
-import typeof UIManager from '../Libraries/ReactNative/UIManager';
 import typeof * as ReactNativeViewConfigRegistry from '../Libraries/Renderer/shims/ReactNativeViewConfigRegistry';
 import typeof flattenStyle from '../Libraries/StyleSheet/flattenStyle';
 import type {DangerouslyImpreciseStyleProp} from '../Libraries/StyleSheet/StyleSheet';
@@ -80,9 +79,6 @@ module.exports = {
   get TextInputState(): TextInputState {
     return require('../Libraries/Components/TextInput/TextInputState').default;
   },
-  get UIManager(): UIManager {
-    return require('../Libraries/ReactNative/UIManager').default;
-  },
   get fabricUIManager(): ?FabricUIManager {
     return require('../Libraries/ReactNative/FabricUIManager').getFabricUIManager();
   },

packages/react-native/src/react-private-interface.js.flow

@@ -27,7 +27,6 @@ export {default as RCTEventEmitter} from '../Libraries/EventEmitter/RCTEventEmit
 export * as ReactNativeFeatureFlags from './private/featureflags/ReactNativeFeatureFlags';
 export * as ReactNativeViewConfigRegistry from '../Libraries/Renderer/shims/ReactNativeViewConfigRegistry';
 export {default as TextInputState} from '../Libraries/Components/TextInput/TextInputState';
-export {default as UIManager} from '../Libraries/ReactNative/UIManager';
 declare export const fabricUIManager: ?FabricUIManager;
 export {default as deepDiffer} from '../Libraries/Utilities/differ/deepDiffer';
 export {default as deepFreezeAndThrowOnMutationInDev} from '../Libraries/Utilities/deepFreezeAndThrowOnMutationInDev';