Stopping ASMR before it plays all night
Updated
Why bother
A video left running all night does three things you did not ask for. It keeps playing sound into a room where you are trying to be asleep, and autoplay will eventually move on to something with a different volume and a different mood. It holds your phone awake, which drains the battery and warms it up under a pillow. If you are on mobile data rather than home internet, it spends that too.
A timer solves all three at once, and every device has one built in. You do not need an app.
On an iPhone or iPad
Open the Clock app and choose Timer. Set the length you want, then tap the row labelled When Timer Ends and scroll all the way to the bottom of the list, past every ringtone, to the option called Stop Playing. Choose that, start the timer, and go back to your video. When the timer runs out, the sound stops instead of an alarm going off.
This works for anything making sound, not only YouTube, so the same trick covers a music app or a podcast.
On an Android phone
Android varies by manufacturer, so there are two routes. Many phones have a sleep timer inside the Clock app under Bedtime or in the media player's own menu. Failing that, the YouTube app has its own: tap your profile picture, open Settings, then General, and look for Sleep timer.
Some phones also have a Modes or Bedtime mode that mutes media at a set hour. That is a blunter tool, but it does the job if you fall asleep at roughly the same time each night.
On a computer
The simplest answer on a laptop is to not use autoplay: turn the autoplay switch off in the player so the video ends when it ends, and pick something long enough to see you to sleep. Many ASMR videos are an hour or more precisely for this.
If you want the machine itself to stop, both Windows and macOS can be told to sleep after a set idle time in their power settings, though a playing video often counts as activity and holds them awake. The phone timer is the more reliable of the two.
Pick the right video for the last hour of the day
Whatever timer you set, the video matters. Look for a long, even one with no sudden volume changes, no bright music at the start and no loud outro. Browse the sleep aid category, which is filtered for exactly this kind of slow, unhurried video.