The adult setting is only used for (hardcore) pornography and that certainly doesn't apply to Nightbitch.

Is there a way to tell if a movie is R rated using the API?

I'm not that familiar with the API, but the R-Rating is entered in the release section, if you can access that over the API: https://www.themoviedb.org/movie/728949-nightbitch/edit?active_nav_item=release_information

@Voyvoda_LLC said:
Is there a way to tell if a movie is R rated using the API?

Hello. I'm going to butt in on this conversation. :-)
The age ratings here on TMDb are called Certification.
To be different from Rating, the user vote.

Using Details of a Movie you can get the Certification.
See the list of data that will be in the response
https://developer.themoviedb.org/reference/movie-release-dates

Using Search it is not possible.

But using Discover it is.
https://developer.themoviedb.org/reference/discover-movie
The filters are the first 4 in the list.

certification - string
use in conjunction with region

certification.gte - string
use in conjunction with region

certification.lte - string
use in conjunction with region

certification_country - string
use in conjunction with the certification, certification.gte and certification.lte filters