Does anyone know how to pause the video by itself?

Video is not interactive. Specialized video players like YouTube,  DVD's, and a few others can be programmed to respond to chapter markers and cues. Quicktime Player and the windows media player will not respond to chapter markers so the solution to your problem is not in AE or Premiere Pro, it is using an authoring program designed to playback a video. Adding chapter markers in AE will help with some applications, but they won't completely automate the process and the standard media players will not automatically pause at the markers.

As Angie suggested here you could use markers, however I think that once you add markers you would need to export it like  a dvd. After Effects, as far as I'm aware, doesn't do interactivity (clicking a button to play as you suggest here). That's something that Animate can do.

You can use markers as Chapter markers;

https://helpx.adobe.com/after-effects/using/layer-markers-composition-markers.html