Remove NativeMethods exports (Strict API) (#57032)

Summary:

Actions the existing/pending deprecations in the preceding diff.

In our Flow source / Strict TypeScript API, the `NativeMethods` type was already deprecated (differing from D107119545).

Changelog:
[General][Breaking] - **Strict TypeScript API**: Remove legacy `NativeMethods` and `NativeMethodsMixin` types

Differential Revision: D107129357

Author: huntie

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

@@ -37,16 +37,6 @@ import typeof deepFreezeAndThrowOnMutationInDev from '../Utilities/deepFreezeAnd
 import typeof deepDiffer from '../Utilities/differ/deepDiffer';
 import typeof Platform from '../Utilities/Platform';
 
-// Expose these types to the React renderer
-export type {
-  HostInstance as PublicInstance,
-  // These types are only necessary for Paper
-  NativeMethods as LegacyPublicInstance,
-  MeasureOnSuccessCallback,
-  MeasureInWindowOnSuccessCallback,
-  MeasureLayoutOnSuccessCallback,
-} from '../../src/private/types/HostInstance';
-
 export type {PublicRootInstance} from '../ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance';
 export type PublicTextInstance = ReturnType<createPublicTextInstance>;
 

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

@@ -10,16 +10,6 @@
 
 import typeof {createPublicTextInstance as createPublicTextInstanceT} from '../ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance';
 
-export type {
-  HostInstance as PublicInstance,
-
-  // These types are only necessary for Paper
-  NativeMethods as LegacyPublicInstance,
-  MeasureOnSuccessCallback,
-  MeasureInWindowOnSuccessCallback,
-  MeasureLayoutOnSuccessCallback,
-} from '../../src/private/types/HostInstance';
-
 export type {PublicRootInstance} from '../ReactNative/ReactFabricPublicInstance/ReactFabricPublicInstance';
 export type PublicTextInstance = ReturnType<createPublicTextInstanceT>;