How can I confirm macOS received a silent update? I know the whole point of a silent update is that it doesn't require user interaction, but it seems like there should be some way to make sure my computer actually received and applied the update. Is there an update log somewhere that would list the full update history: which version and when it was applied on my specific install of macOS?
Your question did not specify a macOS version, but in macOS Mojave, background updates such as Gatekeeper or MRT (the Apple malware removal tool) will typically show in System Information.app -> Software -> Installations.  



Source: About background updates in macOS Mojave