chore: RN 0.71.0 for TestsExample (#1679)

## Description

Should be merged to
#1631.

Build status:

* [x] Android
* [x] iOS

## Changes

Mostly followed up instructions from [upgradle
helper](https://react-native-community.github.io/upgrade-helper/?from=0.70.1&to=0.71.0-rc.6)
with some minor tweaks (ts configuration, etc.)


## Test code and steps to reproduce

Run `TestsExample`

## Checklist

- [ ] Ensured that CI passes

FabricTestExample/android/build.gradle

@@ -4,10 +4,11 @@ buildscript {
     ext {
         buildToolsVersion = "33.0.0"
         minSdkVersion = 21
-        compileSdkVersion = 31
-        targetSdkVersion = 31
+        compileSdkVersion = 33
+        targetSdkVersion = 33
         // ndkVersion = "21.4.7075529"
         ndkVersionn = "23.1.7779620"
+        kotlinVersion = "1.6.21"
     }
     repositories {
         google()
@@ -16,24 +17,6 @@ buildscript {
     dependencies {
         classpath("com.android.tools.build:gradle:7.3.1")
         classpath("com.facebook.react:react-native-gradle-plugin")
-        classpath("de.undercouch:gradle-download-task:5.0.1")
-        // NOTE: Do not place your application dependencies here; they belong
-        // in the individual module build.gradle files
-    }
-}
-
-allprojects {
-    repositories {
-        maven {
-            // All of React Native (JS, Obj-C sources, Android binaries) is installed from npm
-            url("$rootDir/../node_modules/react-native/android")
-        }
-        maven {
-            // Android JSC is installed from npm
-            url("$rootDir/../node_modules/jsc-android/dist")
-        }
-        mavenCentral()
-        google()
-        maven { url 'https://www.jitpack.io' }
+        classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlinVersion"
     }
 }

TestsExample/.gitignore

@@ -62,3 +62,6 @@ buck-out/
 # Ruby / CocoaPods
 /ios/Pods/
 /vendor/bundle/
+
+# Temporary files created by Metro to check the health of the file watcher
+.metro-health-check*

TestsExample/.ruby-version

@@ -0,0 +1 @@
+2.7.6

TestsExample/Gemfile

@@ -1,6 +1,6 @@
 source 'https://rubygems.org'
 
 # You may use http://rbenv.org/ or https://rvm.io/ to install and use this version
-ruby '2.7.4'
+ruby File.read(File.join(__dir__, '.ruby-version')).strip
 
-gem 'cocoapods', '~> 1.11', '>= 1.11.2'
+gem 'cocoapods', '~> 1.11', '>= 1.11.3'