I tested the whole thing again and initially encountered the same problem as you. With the Stretch Image and a Pi 3, there were no problems at all. It also found the external hard drive with the Buster image and a Pi 3. But with a Pi 4, the drive was not recognised.
However, I have now discovered that in my case it was probably due to the power supply unit. I had used a USB-C cable, which didn’t seem to supply enough power to both the Pi 4 and the hard drive. With a different cable, the whole thing worked.
Could the power supply possibly also be the reason in your case?