Wake on Lan doesn't work because the deck going to sleep seems to put the dock to sleep, the Ethernet lights turn off
I solved both using a smart plug. I have a Sonoff (S40 Lite) and a TP-Link Kasa, both have Python packages to control via terminal which led me to choose them.
To enable Power on AC attach:
Shutdown the steam deck fully (not sleep). Hold Volume '+' button and power on to go to BIOS. Go to setup, power, Power on AC Attach and enable.
I set up SSH keys for the steam deck from my phone using Termux on Android. I power it off using an ssh command from my termux, then use a python command to turn off the smart plug as well (you can use the web app or smartphone app just as well, using python just let's me link it all into one command)
To turn on, I just turn on the smart plug and seems to fix the HDMI black screen issue too!
The HDMI issue seems to be fixed in the main update channel, although there's an equally annoying bug where home/overlay menus stop working while you have bluetooth controllers connected.
Hm no luck for me - I'm using a BenQ gaming projector so I'm not sure if TVs and Projectors behave differently in terms of HDMI. Sometimes I still need to "power cycle" the AC adapter to get an image after just switching from gaming mode to desktop mode