Дело не в среде скорее всего, а в версии андроид, вам
if TJBuild_VERSION.JavaClass.SDK_INT >= 30 then
begin
if TJEnvironment.JavaClass.isExternalStorageManager = false then
begin
Intent := TJIntent.Create;
Intent:= TJIntent.JavaClass.init(TJSettings.JavaClass.ACTION_MANAGE_APP_ALL_FILES_ACCESS_PERMISSION);
intent.setData(TJnet_Uri.JavaClass.parse(StringToJString('package:').concat(TAndroidHelper.Context.getPackageName)));
if intent.resolveActivity(TAndroidHelper.Context.getPackageManager) <> nil then
TAndroidHelper.Context.startActivity(Intent);
end;
end;
if TJBuild_VERSION.JavaClass.SDK_INT <= 29 then
begin
FPermissionReadExternalStorage := JStringToString(TJManifest_permission.JavaClass.READ_EXTERNAL_STORAGE);
FPermissionWriteExternalStorage := JStringToString(TJManifest_permission.JavaClass.WRITE_EXTERNAL_STORAGE);
AppPermissions := AppPermissions + [FPermissionReadExternalStorage] +
[FPermissionWriteExternalStorage];
end;