[0.88-stable] Update react and react-test-renderer versions to 19.3.0

[fabriziocucci]

Summary

Bumps react and react-test-renderer to 19.3.0 on 0.88-stable, to match the React 19.3.0 sync that has been picked into React Native's 0.88-stable.

This is the 0.88-stable counterpart of #249, which made the same change on main.

Why

React Native's 0.88-stable picked the React 19.3.0 sync (react/react-native#58446), which bumps the react-native package's peer dependency:

"peerDependencies": {
-   "react": "^19.2.3"
+   "react": "^19.3.0"
}

This branch still pins react: 19.2.3, so a project scaffolded from the 0.88 template no longer satisfies the peer dependency of the react-native it installs. The template e2e jobs fail in all four configurations (Debug and Release, iOS and Android) while installing the new project:

npm error code ERESOLVE
npm error While resolving: RNTestProject@0.0.1
npm error Found: react@19.2.3
npm error   react@"19.2.3" from the root project
npm error Could not resolve dependency:
npm error peer react@"^19.3.0" from react-native@0.88.0-rc.0

Failing run: https://github.com/react/react-native/actions/runs/34846501953

React Native's scripts/e2e/init-project-e2e.js clones this repository, checks out the branch matching the release branch under test, then rewrites only the @react-native/* scoped dependencies and react-native itself. It never rewrites react, so the pin has to be correct here.

Both halves of the change landed on main on 2026-09-10 (react/react-native#58446 and #249 here). This branch was cut on 2026-09-08, two days earlier, so it missed the bump.

Scope

Only the two version lines change. react-native stays at 0.88.0-rc.0 (it is nightly on main, so this is deliberately not taken from #249) and @types/react is already ^19.2.0 on both branches and is left alone.

-    "react": "19.2.3",
+    "react": "19.3.0",
...
-    "react-test-renderer": "19.2.3",
+    "react-test-renderer": "19.3.0",

Tracked in reactwg/react-native-releases#1412.