Tried to make the title as open as possible but what I mean is: add some things to make the player feel less like the main character and more like another citizen. My idea for this is having the player be the target of shady jobs.
Having another detective NPC who does their own cases, maybe even having it clash with the player. Maybe they recieve a job like the photography or theft jobs and so stalks the player or breaks into their apartment. Maybe they can steal portions of evidence from the player if they own an apartment, causing the case board to br missing until they get it back, or just generally being a nuisance via the stalking by reporting felonies. Perhaps you can get a case to blackmail the detective to force them to drop the case and leave you alone. Players might even be able to find the job notice targeting them and be able to confront the client.
I feel it's hard to be immersed while you're the only person investigating crimes. Sure, very little people in this world likely care about justice, but in bigger cities you might have some people in the same position as you. When you're the protagonist you feel separate from the rest of the world. So being just another detective or being targeted just like the people you target for jobs I think would be a good way of achieving immersion