I went from A to E in November, 2024. I noticed that the shuttle arrives at a point where terminal C and terminal E connect; the shuttle used a switchback ramp set up to get up to the entrance to the terminal, which was actually among some jetBlue gates. I noted that the airside shuttle did in fact run both ways for passengers (which formerly was not the case.
Hopefully Delta cleaned up the situation with rechecking DL to DL bags after clearing customs. When I did this connection a couple of years ago, there were no Delta representatives outside of customs, and the one airport employee I encountered told me that I was "jumping the line" by trying to find a belt to recheck luggage (there were about 300 people in line at a "transfer desk" sign. I ended up walking through the central parking garage to Terminal A and then rechecking my bag at the Delta counter inside A.