Great thread! Former military paramedic here, and I've also given classes on wilderness first aid, including one specific to hunters. Additionally, there was a recent MeatEater podcast addressing how to prepare for and treat (some) injuries possible while recreating out of doors. While I am as happy as anyone to go down the rabbit hole of what and why to carry in your pack, I highly recommend taking a wilderness first aid course if you are a hardcore outdoorsman. Here in Montana, a lot of us are often far from the truck, and without cell phone service. You need to know how to preserve yours or your buddy's life until you can either get to cell service, the truck, or someone can get to you. Here's a short list of what I believe are the essentials to carry for the emergencies. But remember, learn how to use them!
SOF-T tourniquet (I believe this is superior to the CAT-T).
Sam splint + cravats (absolutely awesome for stabilizing an extremity injury)
Wound control: quick clot + kerlex + ace wrap
Halo chest seals (penetrating wounds are more common than you'd guess. you can also use a mountain house wrapper and good tape)
Non-drowsy diphenhydramine (claritin - if an allergic reaction starts, get these down the hatch! can save a life when an epi-pen is not available).
Tylenol/ibuprofen
Latex gloves
This list does not add significant weight if you are backpacking, and if you ask me, is non-negotiable when it comes to gearing up.
I also have a small non-emergency bag similar to many of the kits posted above. Bandaids, alcohol pads, pen-light, more gauze, tweezers, etc.