Definitely I'd get an adapter to take pictures through your spotting scope with a phone. I finally did that and I like it a lot. Say you are watching a moose? You can easily get lots of cool still shots or videos before you stalk in. I like that because its not really disrupting the actual hunt. Minimal weight/cost.
For action shots, having someone else along to play camera man will be better whether they use a camera or a descent phone. If not, a Gopro that you can stick on your head is a compromise. You'll at least get action shots of the kill.
With all this you obviously need to think batteries. I think I normally have 5-6 Gopro batteries. I typically don't need that many but occasionally you find out your camera was left on for 30 minutes of crawling through the brush. Also I sleep with my batteries in my sleeping bag. If I think I'll film in the morning I keep the Gopro or phone in my chest pocket so it's warm when I use it.
Get lots of slow scenery shots and shots of packing up, setting up camp, cooking dinner , etc. A hunt is a journey not a kill shot. You'll have a better video if you document that part well.
For ideas I'd watch Limitless Outdoors. From what I can tell they typically hunt in pairs trading one rifle and camera back and forth. Occasionally they use a Gopro but usually only if it's a solo hunt or the second person is a kid. Gives you an idea what works better. Also they are a good example of making enjoyable videos that ate 90% about the journey not the kill shot.