Similar problem, might help others.
I have a MBP 14" 2021 (Sonoma 14.2.1) and received a used H277HU yesterday.
I tried the monitor and had a similar problem, no picture with the USB-C cable that came with the monitor (Targus SS10 cable, so 3.1 gen2 I guess?). I tried to connect and turn on the monitor and the computer in different order, tried with different cables etc. but nothing worked.
The monitor worked perfectly with a HDMI cable though.
Then I found this thread and played with the F-menu. Did reset from there and what not. Then I decided to try to connect the monitor once more. This time MacOs showed a notification for allowing Cypress Semicoductor USB hub to connect. I hadn't seen that notification during my previous attempts. Clicked Allow and lo and behold, the picture appeared on the monitor perfectly.
I was happy for a while. Even tested that putting the computer to sleep and waking up would turn on the monitor and it worked.
I disconnected and reconnected the monitor and after that it didn't work anymore ... Tried all the things mentioned above, but no luck.
Then I did the firmware update with a PC to see if would help. Everything seemed to go ok. According the updater the Hx3 version stayed in 1.10.0.87 after the update and CCG Device App version increased from 0.1.15 => 0.1.18. But the monitor still didn't work.
As a last resort I run the firmware updater again to see if the update had actually succeeded. The updater said that the Existing CCG Device App version was 0.1.18, but I let the update run through again even though there was already the updated version in the monitor.
After running the firmware update the second time the monitor started to work 🎉
The monitor type in the F-menu is H277HU kmipuz, FW version is 103 (didn't change during the firmware update), and manufacturing date is 170710.
So I guess the lesson here is that the monitor might work in some situations without the (CCG Device App) firmware update, but the firmware update is the key for making it work consistently. And that if the first firmware update doesn't solve the issue, do it again