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You are right to focus on mood via sound design here. Scary/creepy/anxiety-focused games rely heavily on sound to illicit those feelings in your players.

The easiest way to start is by listing out all the "moments" or mechanics your game needs sound effects for. Possible Examples: Footsteps, creaking doors, getting pick-ups, burning fire, building items, destruction/explosions, eating, attack sounds, breathing, leveling-up, etc. Part of good sound design is deciding what needs to be heard and what doesn't, or when something needs to be heard.

Sound effects can achieve 2 things: 1) inform the player of a state change, 2) illicit mood. Great sound design can achieve both simultaneously. For example, imagine your game has a mechanic where the player can freeze to death at night. Every evening, there is a heat bar that fills up if the player gets close to a camp fire and slowly empties the longer a player wanders away from his/her heat source. In that case, you may want your player to hear the crackling sound of fire whenever a player gets close enough to a camp fire to effect his heat bar, and have the sound effect fade the further away she/he/they gets. You might also decide to replace that fire sound with a chilling wind sound to indicate they have wandered too far from their heat source. Without this gameplay mechanic, the crackling fire might be too insignificant to warrant a dedicated sound effect and you may decide that the only time you hear a fire is when you set one so the player can keep their focus to other important sounds.

After you have listed all the sound "moments" that your game needs, start thinking about what emotions or impressions you want to evoke in each instance. For example, when getting a pick-up item you could do the classic gamey thing of using a happy ding/chirp/boop that alerts the player something good has happened, but that might not fit your mood (unless you want it to provide a "hope in the dark" moment). Instead, you might use the sound of, say, fabric rustling to evoke the sense of your player stuffing the item in their pocket or a backpack. Or you might use different sound effects for each pick-up item. A bullet or weapon pick-up might trigger a gun cocking or loading sound, while picking-up food might trigger a munching sound (if you eat it right away) or the sound of your player saying something like "Mmmmm" to remind the player of how hungry they are supposed to be.

If you are going to make your own music, look for instruments that fit the mood you want. This can inspire the way you move forward. Here's a famous example of a horror "instrument" that could provide some inspiration (heavy on the reverb).

I hope this helps, let me know if you have further questions!