Have you tried accessing HA from another device on your network? Any browser should do it at http://homeassistant.local:8123/. It isn’t clear which image you are using, but you wouldn’t normally expect to see anything on the RPi screen.
The unit does not get an IP. By watching the green LED (access to SD) it is only accessing SD a fraction of a second, then it never lights up any more.
Have to agree there. I use a pi4 2gb and run 32 bit. The only reason one would want to run a 64bit system is to access over 3.5gb of RAM.
So use the 32 bit image and make some use of those GPIO pins. Also as @Stiltjack stated you need to access over the network. IMHO both @Stiltjack and @Salmoneus are moving you in the right direction.