How to make an "Obligations" phase interesting

I'm working on an RPG that started as a Blades in the Dark hack, about teenagers solving mysteries in their weird home town. It uses phases of play like Blades or Torchbearer, and one of the three phases is the Obligations phase, where they have to fulfill their duties at work, or school, or with family. Now obviously I don't want to zoom in too much during this time, but I want there to be some more interesting content, beyond "Do you pull your weight or blow it off?", and I'm having trouble figuring out how best to do that.

The Obligation Phase is supposed to do a few things. One, it gives the GM an opportunity to advance their threat clocks and have their threats make moves, to provide hooks when transitioning from Downtime to Investigation. For that reason, I don't want there to be any hands on GM stuff- no scene framing or anything, I want it to mostly be the player making an interesting decision, that should influence the game in a meaningful way. It should also highlight relationships the players have to NPCs, and be focused on how the characters relate to the town and the people in it. I feel like I have these covered already, but barely, but it feels really bland.

Right now, its pretty bare bones. The players get to choose if they "Take it easy" and heal Strain with an NPC, they can "Blow it off" and take Strain with an NPC, but get an extra downtime action, or they can "Pull their weight" and get a special benefit depending on the type of obligation they have (family, work, school, hobby), and roll on a small table with some less-than-interesting results. I'd be happy to provide more information if it helps.

Any ideas or just commentary? Are there any other games with Phases of play that you could direct me to?