According to Logitech’s support page, the problem was caused by “an expired certificate” required for the apps to run.
As reported by The Verge, the Logitech Subreddit saw Mac users complaining that their app wasn't working, and one comment ...
Logitech has released a manual fix for Logi Options Plus and G Hub users on macOS after an expired certificate caused both apps and their built-in updaters to stop working.