I found solution when I a little bit reworked this xamarin-samples solution code:
xamarin/xamarin-forms-samples/DependencyService (thanks to David Britch)
The key moment here is: Intent.ActionOpenDocument intent action for the Android picker.
And now with this code:
public async Task<string> PickFileAsync(FilePickerFileType fileTypeEnum)
{
string pickerType = string.Empty;
string title = string.Empty;
if (fileTypeEnum == FilePickerFileType.Images)
{
pickerType = "image/*";
title = "Select images";
}
else if (fileTypeEnum == FilePickerFileType.Pdf)
{
pickerType = "application/pdf";
title = "Select PDF";
}
else if (fileTypeEnum == FilePickerFileType.Videos)
{
pickerType = "video/*";
title = "Select video";
}
// Define the Intent for getting files
Intent intent = new(Intent.ActionOpenDocument);
intent.SetType(pickerType);
intent.PutExtra(Intent.ExtraLocalOnly, true);
// Start the file-picker activity (resumes in MainActivity.cs)
MainActivity.Instance.StartActivityForResult(
Intent.CreateChooser(intent, title),
MainActivity.PickFileId);
// Save the TaskCompletionSource object as a MainActivity property
MainActivity.Instance.PickFileTaskCompletionSource = new TaskCompletionSource<string>();
// Return Task result
return await MainActivity.Instance.PickFileTaskCompletionSource.Task.ConfigureAwait(false);
}
, I have necessary result, where I don't have any Google Drives in my files browser:

Hopefully, my example will help people to avoid Google Drive video files loading during the video files picking with Xamarin / MAUI apps. Which is cause a lot of loading issues. That's why apps like LinkedIn, Telegram, Viber, Facebook and other mobile apps allow to pick only local device videos from local folders, but not from remote Drives, like Google, to avoid loading issues.