guess it's related to japanese office culture, not sure tho
Some countries like Japan are strict when it comes to quit your job because you have to be loyal to your company. Plus, quitting would mean it'd be a nuisance for your coworkers (more work for them or just disruption of the "team harmony" which is taken seriously there). I guess Korea, where the story is taking place, is one of these countries, which explain why they have to keep it a secret. It's way more chill in a lot of western countries though where there's no (or at least less) sense of loyalty towards the company, and thus it's easier to quit.
I don't understand what's the problem with looking at new jobs on ur job but ok, it's cute