What's happening when the blanking video showed while using LG High-end monitors as the shared monitors with KVM switches?
You have desktop PC which can support the highest range of the resolution and refresh rate the LG monitor can support - using DP 1.4 protocol and timing.
And you have a laptop and the video output can not support/meet the highest range of the resolution and refresh rate of the LG - so after the DisplayPort initial video handshaking between
the laptop and KVM switch + the KVM switch and the monitor - the ultimate protocol was set to using DP 1.2 protocol and timing.
In this case, most of the high-end monitors we had tested will have no problem to provide its internal DP version shifting to adapt the dynamic changing (even their DP version on monitor were set to DP 1.4 or DP 1.2), but LG's firmware and hardware driver did not and can not do internal auto dynamic adjustment for the range of changes and doing it correctly. That's the reason why you need to manually to change the DP1.4 to DP1.2 on the LG monitor.
This recommendation was confirmed with hundreds of KVM switch setup cases that users had been reported since 2019. The blanking screen issue may not be a general issue for all KVM switch products in the market. However, it's the duty of a KVM switch developer and maker to report the compatibility issues found for years.