macOS secure keyboard entry breaks iTerm global hotkey
FYI: Any app enabling “Secure Keyboard Entry” on your Mac (confirmed at least for macOS 14.7) will prevent the iTerm2 global hotkey shortcut from working unless the iTerm2 app is foregrounded.
Details are in this iTerm GitHub issue. Fortunately for me, for some reason BetterTouchTool happens to tell you which app has enabled secure keyboard entry. So you can search and destroy it and get your global iTerm hotkey working again.