I was playing tower of mask and thinking about this exact issue: VS heavy focus on combat that is boils down to "mouse click until enemy falls over".
I think just adding critical hits would help a lot - they reward good aim, they reward staying calm, instantly weapon reach starts to matter more, it could tie into lore with the drifters and would make hunting more interesting.
A breakdown how I would imagine a simple, quick implementation that would still be rewarding and add depth:
A critical hitbox is added to each enemy, it can be head for a rabbits and wolves, heart for bears, deer and maybe drifters, torso for boars etc.
Upon hitting the critical hitbox, the feedback would be the hit sound pitched differently and enemy flashing white. They could also stagger for longer giving even more advantage to players.
The damage would be multiplied depending on weapon type, maybe even depending on whether enemy was aware of you making it important to be sneaky while hunting.
As a result you would have a system where when fighting the horrors you have a way to finish the combat quicker or stagger the enemy in order to get in more hits or buy more time to run away. Bow close combat would be vastly more difficult and it would incentivize spending an inventory slot for a melee weapon.
Hunting would reward accuracy and stealth cause you could catch a deer with a shot into the heart rather than chase after it while spamming arrows or cheese it with a pit.