I don't have a solution you want but I use a mobile app called "Just watch" to search for any new (or old) thing I want to watch and see where it is available.
For example, I wanted to watch Lord of the Rings so I went in app and searched for it (first movie) and as you can see below it is available on Netflix and Prime for me to watch.
View attachment 89433
This is all manual activity and used only on need basis. Also it works with tv shows.
But I would like to highlight something here. You are saying you will delete the movie from NAS if it is available on OTT but movies and shows keep coming and going on OTT. So some movie you see on Netflix today, there is no guarantee that it will be available next month. All depends on how they have struck deals with the movie houses.