The same problem: On connecting with LG display (LG-27UL850W), the display connection can't be established.
We have about 20 MacBooks and MacBook Airs (various ages) running OSX, and about 32 LG monitors.
Both Ventura and Sonoma installs experience the same behaviour.
Things we tried, without success:
Turning it off and on again (both computer and display)
Switch USB-C cables with a working monitor.
Use other USB-C port on the computer.
Add additional power adapter to the computer.
Upgraded from Ventura to Sonoma.
I've seen an error in Console.app on attempting to connect to a display that fails to connect.
kernel (AppleDisplayCrossbar)
Subsystem: -- Category: <Missing Description> Hide
Activity ID: 0
Thread ID: 0×357d19
PID: 0
Volatile ERROR
2023-10-05 09:31:15.490449+0200
IOAV[165125] AppleATCDPAltModePort(atc0-dpphy)<0x1000002b8>::handleActivate: DP Alt Mode with PHY still in use
Maybe needless to say, but this greatly disrupts our work.