I was able to fix the issue by using System.Windows.Forms.Clipboard instead of System.Windows.Clipboard.

Explanation:

System.Windows.Clipboard uses WPF. Its first usage will start a hidden WPF message loop. This loop marks the application as DPI-aware and triggers a DPI awareness context switch. As a result, the window layout breaks if the application cannot handle higher DPI settings.
To reproduce the behavior, a Windows DPI setting above 100% is required (e.g., 150%).