Remove deprecated Libraries/ReactPrivate forwarding modules

Summary:
The `react-private-interface` and `setup-env` entry points now provide the private contract between React and React Native that `Libraries/ReactPrivate/` forwarded to, so the deprecated forwarding modules can be removed.

**This diff**

- Delete `Libraries/ReactPrivate/` — `ReactNativePrivateInterface`, `ReactNativePrivateInitializeCore`, and their `.flow`/`README` files.
- Repoint internal `packages/react-native` imports directly at their source modules instead of the `react-private-interface` aggregator: `AnimatedProps` and two integration tests now import `getNodeFromPublicInstance` from `ReactFabricPublicInstance`, and `index.js.flow` re-exports `PublicRootInstance`/`PublicTextInstance` from there (adding a `PublicTextInstance` export to that module).
- Repoint the remaining consumers at the `react-native/react-private-interface` entry point.
- Drop the stale `Libraries/ReactPrivate/ReactNativePrivateInterface` entries from the eslint and Flow-codemod `publicAPIMapping`s and the `rn-arch` migration-list filters.

Changelog: [Internal]

Differential Revision: D114055938

Author: huntie

packages/eslint-plugin-react-native/utils.js

@@ -519,10 +519,6 @@ const publicAPIMapping = {
     default: null,
     types: ['ErrorUtils'],
   },
-  'Libraries/ReactPrivate/ReactNativePrivateInterface': {
-    default: null,
-    types: ['PublicRootInstance', 'PublicTextInstance'],
-  },
 };
 
 module.exports = {

packages/react-native/Libraries/Animated/nodes/AnimatedProps.js

@@ -16,8 +16,8 @@ import type {AnimatedStyleAllowlist} from './AnimatedStyle';
 import NativeAnimatedHelper from '../../../src/private/animated/NativeAnimatedHelper';
 import * as ReactNativeFeatureFlags from '../../../src/private/featureflags/ReactNativeFeatureFlags';
 import {getFabricUIManager} from '../../ReactNative/FabricUIManager';
+import {getNodeFromPublicInstance} from '../../ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance';
 import {findNodeHandle} from '../../ReactNative/RendererProxy';
-import {getNodeFromPublicInstance} from '../../ReactPrivate/ReactNativePrivateInterface';
 import flattenStyle from '../../StyleSheet/flattenStyle';
 import {AnimatedEvent} from '../AnimatedEvent';
 import AnimatedNode from './AnimatedNode';

packages/react-native/Libraries/ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance.js

@@ -55,6 +55,8 @@ export function createPublicTextInstance(
   return new ReadOnlyText(internalInstanceHandle, ownerDocument);
 }
 
+export type PublicTextInstance = ReturnType<typeof createPublicTextInstance>;
+
 export function getNativeTagFromPublicInstance(
   publicInstance: ReactNativeElement,
 ): number {

packages/react-native/Libraries/ReactPrivate/README

@@ -4,7 +4,7 @@
  * This source code is licensed under the MIT license found in the
  * LICENSE file in the root directory of this source tree.
  *
- * @generated SignedSource<<590f18ec6caea33fef591da5d56419f4>>
+ * @generated SignedSource<<b1273b105161b7b40e5571f4235a4812>>
  *
  * This file was generated by scripts/js-api/build-types/index.js.
  */
@@ -1823,7 +1823,6 @@ declare function createPublicTextInstance(
   internalInstanceHandle: InternalInstanceHandle,
   ownerDocument: ReactNativeDocument_default,
 ): ReadOnlyText_default
-declare type createPublicTextInstanceT = typeof createPublicTextInstance
 declare type CursorValue = "auto" | "pointer"
 declare type DataDetectorTypesType =
   | "address"
@@ -3705,7 +3704,7 @@ declare type ProgressBarAndroidProps =
 declare type PublicRootInstance = symbol & {
   __PublicRootInstance__: string
 }
-declare type PublicTextInstance = ReturnType<createPublicTextInstanceT>
+declare type PublicTextInstance = ReturnType<typeof createPublicTextInstance>
 declare interface PushNotification {
   finish(result: string): void
   getAlert(): (Object | undefined) | (string | undefined)
@@ -5941,7 +5940,7 @@ export {
   ProgressBarAndroidInstance, // ab545ef1
   ProgressBarAndroidProps, // 6484d368
   PublicRootInstance, // 8040afd7
-  PublicTextInstance, // 6937c7bf
+  PublicTextInstance, // 16c26204
   PushNotificationEventName, // 84e7e150
   PushNotificationIOS, // b4d1fe78
   PushNotificationPermissions, // c2e7ae4f

packages/react-native/Libraries/ReactPrivate/ReactNativePrivateInitializeCore.js

@@ -497,7 +497,7 @@ export type {ErrorUtils} from './Libraries/vendor/core/ErrorUtils';
 export type {
   PublicRootInstance,
   PublicTextInstance,
-} from './Libraries/ReactPrivate/ReactNativePrivateInterface';
+} from './Libraries/ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance';
 
 export type {
   EventSubscription,

packages/react-native/Libraries/ReactPrivate/ReactNativePrivateInterface.js

@@ -14,7 +14,7 @@ import '@react-native/fantom/src/setUpDefaultReactNativeEnvironment';
 import type {Node} from '../../../../../Libraries/Renderer/shims/ReactNativeTypes';
 import type {HostInstance} from 'react-native';
 
-import {getNodeFromPublicInstance} from '../../../../../Libraries/ReactPrivate/ReactNativePrivateInterface';
+import {getNodeFromPublicInstance} from '../../../../../Libraries/ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance';
 import isUnreachable from '../isUnreachable';
 import {
   createShadowNodeReferenceCounter,