Thanks for your comment and I appreciate you trying to save me time by sending the APK but I'm afraid I don't download APKs unless they are from Google Play. I implemented the app by hand from your blocks diagram to ensure I hadn't missed anything and with the file options in Designer set to Shared scope and with the read and write permissions ticked. The app didn't work on Android 11. On pressing the 'Save' button it produced an error 908 "The Permission Write_ExternalStorage has been denied". I believe this is because the leading forward stroke on your file path invokes the Android 10 Legacy option.
Reference: Storage (used in my first post)
"Legacy: Files will be read from and written to the file system using the App Inventor rules prior to release nb187. That is, file names starting with a single / will be read from and written to the root of the external storage directory, e.g., /sdcard/. Legacy functionality will not work on Android 11 or later."
Reference: Storage updates in Android 11 | Android Developers (used in Nishyanth's post, marked intended behaviour).
"Apps that run on Android 11 but target Android 10 (API level 29) can still request the requestLegacyExternalStorage attribute. This flag allows apps to temporarily opt out of the changes associated with scoped storage, such as granting access to different directories and different types of media files. After you update your app to target Android 11, the system ignores the requestLegacyExternalStorage flag."
The original question remains open. The AI2 File component is unable to read or write shared text files in the Download and Document media folders with the current version of Android 11. Is this a bug or is it intended?".