pause video with overlay ffmpeg
Let's call the video frame rate F. And the start time of the overlay t

Use

ffmpeg -i in.mp4 -i ol.png -filter_complex
         "[0]trim=0:t,loop=X*F:1:t*F,setpts=N/FRAME_RATE/TB[fol];
          [0]trim=t,setpts=N/FRAME_RATE/TB[post]
          [fol][1]overlay[pre];[pre][post]concat" out.mp4


The loop filter accepts frame index numbers, so you have to convert your start time and loop time to frame counts and substitute with those values.