While You certainly need an aerobic base and running can play a part in that, particular if you cycle it, My issues with running in general, particularly running 30-40 miles a week year around, is that it’s catabolic. Since rucking uphill with a pack is a muscular endurance event, you’re only going to stand to benefit from being considerably stronger than the typical runner. Ideally, running would be subordinate to other areas of fitness as it relates to hunting. If you are an actual runner, that’s your primary thing and you do races, that all look different, but a person who uses running as their primary means of training for backcountry hunting is likely going to be lacking in the muscular endurance department since that it a different energy pathway.
I do have a hunting and backcountry snowboarding partner that’s an mountain ultra racer. We put on camelbacks and go peak bagging, he’s hard for me to keep up with. His zone 2 is easily zone 3 for me (he’s also 10 years younger) and he’s often ~200+ yards out in front of me and I’m working hard to keep up. No doubt his cardiovascular system is better conditioned than mine. HOWEVER, we strap on 35# packs and do an overnight scouting trip, this scenario is reversed and I’m 200 yards out in front climbing to a glassing point at 12,800 with packs on and he’s the one struggling to keep up. The primary adaptation there is muscular endurance, not “cardio” like it is intuitive to believe and certainly nothing to do with getting your lungs “in shape” (is that is anything more than en expression).
That’s not to dismiss the fact that you need an aerobic base in order to achieve proper muscular endurance, but that base serves entirely subordinate to muscular endurance. If you are already strong, muscular endurance will come fairly quickly. In conjunction with strength training and some aerobic baseline maintenance, it’s something that can be effectively achieved by training it just once a week: uphill rucking in zone 2. Surplus strength will contribute considerably to continued performance after fatigue sets in (numerous studies to support this claim) and trying to build strength and muscular endurance at the same time is entirely inefficient.
As is the case in all of these threads, my advice is always the same: “get strong first” -some part of your year should ideally be dedicated to pure strength training. With studies suggesting that you otherwise lose ~1% of your muscle mass annually after the age of 40, if nothing else, you should be thinking about longevity and how you don’t want to end up. If you wake up at 50 and find yourself with 10% less muscle than you had at 40 and you weren’t very strong to begin with, you’re on the verge of serious decline and you’re going to have a much more difficult time realizing muscular endurance.