At 4:20 I wasn't very careful with my words or graphics. For those familiar, I made the decision to skip over the idea of "proper distance" for simplicity in this video.
This is the distance between us and the object (in this case GS-z13) when the light was emitted, which at the time was actually 2.34 billion light years.
The universe's expansion means that the light travel time is then the longer "lookback distance" of 13.48 billion light years.