Im also facing the same issue. using HDMI and LG monitor.
Process: WindowServer [87]
Path: /System/Library/PrivateFrameworks/SkyLight.framework/Versions/A/Resources/WindowServer
Load Address: 0x1005c4000
Identifier: WindowServer
Version: 600.00 (762.11)
Code Type: ARM64E
Platform: macOS
Parent Process: launchd [1]
Date/Time: 2023-05-13 21:11:17.874 +0200
Launch Time: 2023-05-13 16:46:49.830 +0200
OS Version: macOS 13.3.1 (22E261)
Report Version: 7
Analysis Tool: /usr/bin/sample
Physical footprint: 652.8M
Physical footprint (peak): 1.2G
Idle exit: untracked