[compiler][be] Make program traversal more readable (#33147)

React Compiler's program traversal logic is pretty lengthy and complex
as we've added a lot of features piecemeal. `compileProgram` is 300+
lines long and has confusing control flow (defining helpers inline,
invoking visitors, mutating-asts-while-iterating, mutating global
`ALREADY_COMPILED` state).

- Moved more stuff to `ProgramContext`
- Separated `compileProgram` into a bunch of helpers

Tested by syncing this stack to a Meta codebase and observing no
compilation output changes (D74487851, P1806855669, P1806855379)
---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/facebook/react/pull/33147).
* #33149
* #33148
* __->__ #33147

DiffTrain build for [5069e18](5069e18)

Author: mofeiZ

compiled-rn/VERSION_NATIVE_FB

@@ -1 +1 @@
-19.2.0-native-fb-9518f118-20250508
+19.2.0-native-fb-5069e180-20250509

compiled-rn/facebook-fbsource/xplat/js/RKJSModules/vendor/react/react-dom/cjs/ReactDOM-dev.js

@@ -7,7 +7,7 @@
  * @noflow
  * @nolint
  * @preventMunge
- * @generated SignedSource<<9ce20965cef4ec7444a6a12df471be69>>
+ * @generated SignedSource<<21b1f8e6089cbb476b1038e0ba671b36>>
  */
 
 "use strict";
@@ -404,5 +404,5 @@ __DEV__ &&
     exports.useFormStatus = function () {
       return resolveDispatcher().useHostTransitionStatus();
     };
-    exports.version = "19.2.0-native-fb-9518f118-20250508";
+    exports.version = "19.2.0-native-fb-5069e180-20250509";
   })();

compiled-rn/facebook-fbsource/xplat/js/RKJSModules/vendor/react/react-dom/cjs/ReactDOM-prod.js

@@ -7,7 +7,7 @@
  * @noflow
  * @nolint
  * @preventMunge
- * @generated SignedSource<<b0cc0f4456efbea270f20c9ea825fc77>>
+ * @generated SignedSource<<ae7b6331472147d7c231276b59e62233>>
  */
 
 "use strict";
@@ -203,4 +203,4 @@ exports.useFormState = function (action, initialState, permalink) {
 exports.useFormStatus = function () {
   return ReactSharedInternals.H.useHostTransitionStatus();
 };
-exports.version = "19.2.0-native-fb-9518f118-20250508";
+exports.version = "19.2.0-native-fb-5069e180-20250509";

compiled-rn/facebook-fbsource/xplat/js/RKJSModules/vendor/react/react-dom/cjs/ReactDOM-profiling.js

@@ -7,7 +7,7 @@
  * @noflow
  * @nolint
  * @preventMunge
- * @generated SignedSource<<b0cc0f4456efbea270f20c9ea825fc77>>
+ * @generated SignedSource<<ae7b6331472147d7c231276b59e62233>>
  */
 
 "use strict";
@@ -203,4 +203,4 @@ exports.useFormState = function (action, initialState, permalink) {
 exports.useFormStatus = function () {
   return ReactSharedInternals.H.useHostTransitionStatus();
 };
-exports.version = "19.2.0-native-fb-9518f118-20250508";
+exports.version = "19.2.0-native-fb-5069e180-20250509";