I had similar problems after attempting to use the same method of putting the EDGE-V into Upgrade Mode. That button sequence is almost the same as the sequence that erases the eMMC, which results in no HDMI output. Here’s a link detailing that discussion:
https://forum.khadas.com/t/user-manual-prototype-for-khadas-beginners/5767/15
I was more successful with using the TST method: Power on, then 3 presses of the Function button within 2 seconds. Then, AndroidTool detects the SBC as being in Maskrom mode. You should be able to Upgrade the firmware from there.
Also, you need to use the USB-C connector located next to the HDMI for connecting the EDGE-V to your PC. The USB-C beneath the USB2 connector is only for power input. I also needed to utilize that power input, instead of relying on the PC’s USB for powering the EDGE-V.
Please let me know whether this solves your issue, because as you can see from my previous comments, I’m having HDMI sync issues with Khadas’ Ubuntu eMMC images, but not on SD card.