[RN] Move new event dispatching pipeline to RN (#36266)

## Summary

We found a bug in the logic in
https://github.com/facebook/react/pull/36253 and we realized it's very
inconvenient to iterate on the implementation when it's in this
repository, as we're forced to then synchronize it to RN to test
changes.

This moves the entire implementation to RN for simplicity and also to
simplify some clean ups in the future (like removing `top` prefixes from
native event types).

## How did you test this change?

The changes are gated. Will test e2e in RN.

scripts/flow/react-native-host-hooks.js

@@ -204,13 +204,10 @@ declare module 'react-native/Libraries/ReactPrivate/ReactNativePrivateInterface'
   declare export function getInternalInstanceHandleFromPublicInstance(
     publicInstance: PublicInstance,
   ): ?Object;
-  declare export function dispatchTrustedEvent(
+  declare export function dispatchNativeEvent(
     target: EventTarget,
-    event: Event,
-  ): void;
-  declare export function setEventInitTimeStamp(
-    eventInit: {[string]: mixed},
-    timeStamp: number,
+    type: string,
+    eventData: {[string]: mixed},
   ): void;
   declare export function createAttributePayload(
     props: Object,