I'm also having this problem.
My setup is Mac Studio 2022, OSX 12.6.2, 2x LG 4k displays connected via USB-C.
Tried different cables, monitor settings, display settings and no luck.
Do a reboot or a shut down, power on, my second screen doesn't power up, stays asleep. When the computer powers back up, to get second screen back, I unplug it from power, and plug back in and it works again. VERY frustrating, as doing a reboot remotely means I can't get my second monitor up and running. Will try the above software.