There are still no smart albums on an iPhone. And the Filters do not support the albums as well.
To be able to see which photos are in albums you would have to mark the photos you added to albums. I am only adding favourites to albums, as I do not want to clutter the albums up with mediocre photos. Albums are getting useless, when they are holding too many photos and need scrolling. The favorites are easily recognised by the heart ♡ badge overlay.
Another way to see which photos you have organized would be to use the Shared iCloud Photos Library to split your library into a personal library (with the photos that need organising) and a Shared library for the photos you are done with. Move all photos from your albums into the Shared iCloud Photos Library. See: How to use iCloud Shared Photo Library – Apple Support (UK)
Then you can toggle between your unorganized mess and the organized photos by switching between your personal library and the Shared iCloud Photos Library. This will work, if all your devices are supporting the Shared iCloud Photos Library. I am not sharing my iCloud Photos Library with others, just with myself between my two Apple IDs and enjoy to have two different libraries in iCloud this way. This will not work, if you invite others to share your library. But if you are the only user, it is great, as we can have two different libraries in iCloud and switch between them.