While it shouldn’t be necessary to resort to third party services to resolve these issues, it’s worth noting that JustWatch will tell you where a movie can be found and Letterboxd (among others) will give you a somewhat more clunky unified watchlist.
If you put your unified watchlist on JustWatch, they will even notify you when something you want to watch becomes available.
As far as "third party service shouldn't be necessary", is it that different from getting the TV Guide in the 80s or 90s to find out when a show was going to be on TV?