The urgency thing immediately makes me think of Cyberpunk 2077. The initial quest line sets it up that you must fix TERRIBLE_NARRATIVE_PROBLEM or you will die in a couple of weeks, but in fact passage of time doesn't matter at all and if you just follow the main quest line with the urgency the narrative demands of you, you'll miss 90% of the game's content and probably have a really terrible time because you'll be underpowered compared to all the end boss stuff.