Recently iOS included a native noise generator that bypasses the need for external services like Spotify or websites. It offers six different kinds of noise to listen to on your phone.
It’s in the iPhone control center under the ear icon (which you may have to enable). The feature is called ‘background sounds’.
It's not really the kind of audio that you'd be able to notice looping. The white/pink/brown noise files are each a minute long, and the stream/ocean/rain sounds are comprised of 17-20 sound files between 1-3 minutes long (and I'm guessing it randomizes the playback order).
It’s in the iPhone control center under the ear icon (which you may have to enable). The feature is called ‘background sounds’.