[local_auth] Replace `USE_FINGERPRINT` to `USE_BIOMETRIC` post deprecation in example and README (#6032)

diff --git a/packages/local_auth/local_auth/CHANGELOG.md b/packages/local_auth/local_auth/CHANGELOG.md
index 1aae73d..975d171 100644
--- a/packages/local_auth/local_auth/CHANGELOG.md
+++ b/packages/local_auth/local_auth/CHANGELOG.md
@@ -1,3 +1,7 @@
+## 2.1.1
+
+* Replaces `USE_FINGERPRINT` permission with `USE_BIOMETRIC` in README and example project.
+
 ## 2.1.0
 
 * Adds Windows support.
diff --git a/packages/local_auth/local_auth/README.md b/packages/local_auth/local_auth/README.md
index 3077f8e..a68692e 100644
--- a/packages/local_auth/local_auth/README.md
+++ b/packages/local_auth/local_auth/README.md
@@ -235,12 +235,12 @@
 ### Permissions
 
 Update your project's `AndroidManifest.xml` file to include the
-`USE_FINGERPRINT` permissions:
+`USE_BIOMETRIC` permissions:
 
 ```xml
 <manifest xmlns:android="http://schemas.android.com/apk/res/android"
           package="com.example.app">
-  <uses-permission android:name="android.permission.USE_FINGERPRINT"/>
+  <uses-permission android:name="android.permission.USE_BIOMETRIC"/>
 <manifest>
 ```
 
diff --git a/packages/local_auth/local_auth/example/android/app/src/main/AndroidManifest.xml b/packages/local_auth/local_auth/example/android/app/src/main/AndroidManifest.xml
index 8c09177..4acc4eb 100644
--- a/packages/local_auth/local_auth/example/android/app/src/main/AndroidManifest.xml
+++ b/packages/local_auth/local_auth/example/android/app/src/main/AndroidManifest.xml
@@ -2,7 +2,7 @@
     package="io.flutter.plugins.localauthexample">
 
     <uses-permission android:name="android.permission.INTERNET"/>
-    <uses-permission android:name="android.permission.USE_FINGERPRINT"/>
+    <uses-permission android:name="android.permission.USE_BIOMETRIC"/>
 
     <application android:label="local_auth_example" android:icon="@mipmap/ic_launcher">
         <activity android:name="io.flutter.embedding.android.FlutterFragmentActivity"
diff --git a/packages/local_auth/local_auth/pubspec.yaml b/packages/local_auth/local_auth/pubspec.yaml
index a555150..c6315c5 100644
--- a/packages/local_auth/local_auth/pubspec.yaml
+++ b/packages/local_auth/local_auth/pubspec.yaml
@@ -3,7 +3,7 @@
   authentication via fingerprint, touch ID, face ID, passcode, pin, or pattern.
 repository: https://github.com/flutter/plugins/tree/main/packages/local_auth/local_auth
 issue_tracker: https://github.com/flutter/flutter/issues?q=is%3Aissue+is%3Aopen+label%3A%22p%3A+local_auth%22
-version: 2.1.0
+version: 2.1.1
 
 environment:
   sdk: ">=2.14.0 <3.0.0"
diff --git a/packages/local_auth/local_auth_android/example/android/app/src/main/AndroidManifest.xml b/packages/local_auth/local_auth_android/example/android/app/src/main/AndroidManifest.xml
index 8c09177..4acc4eb 100644
--- a/packages/local_auth/local_auth_android/example/android/app/src/main/AndroidManifest.xml
+++ b/packages/local_auth/local_auth_android/example/android/app/src/main/AndroidManifest.xml
@@ -2,7 +2,7 @@
     package="io.flutter.plugins.localauthexample">
 
     <uses-permission android:name="android.permission.INTERNET"/>
-    <uses-permission android:name="android.permission.USE_FINGERPRINT"/>
+    <uses-permission android:name="android.permission.USE_BIOMETRIC"/>
 
     <application android:label="local_auth_example" android:icon="@mipmap/ic_launcher">
         <activity android:name="io.flutter.embedding.android.FlutterFragmentActivity"