Buried down in the comments was a technical fix suggested by torstenvl.
Safari has a few configuration entries accessible via
defaults read com.apple.coreservices.uiagent.
While I haven’t tested this personally,
torstenvl recommended stubbing out the notification with the following commands:
defaults write com.apple.coreservices.uiagent CSUIHasSafariBeenLaunched -bool YES defaults write com.apple.coreservices.uiagent CSUIRecommendSafariNextNotificationDate -date 2050-01-01T00:00:00Z defaults write com.apple.coreservices.uiagent CSUILastOSVersionWhereSafariRecommendationWasMade -float 99.99
If this works for you, let me know. I’m currently running the macOS Monterey beta at the time of writing and as I’ve already used Safari, I don’t believe I get this notification anymore.