You are full of contradictions here that you have to resolve. That doesn't mean I am critiquing your decision on dogs, it just means you have things in this list that can't be reconciled.

You want a gun dog? Excellent! They are amazing animals and will serve you well. But then they will NOT have a medium exercise regimen. Not even close. They'll be at the top of the spectrum. ANY working dog requires a lot of exercise as a minimum, and a huge amount as standard. So...if you want to hunt with your dogs, and you want a gun breed, you better get ready to spending AT LEAST an hour (probably a lot more) a day with them. I mean, absolute minimum. As in, if you skip a day they will eat your couch.

Moreover, you want to train a gun dog? Do you know how? Do you have a trainer lined up? Are you planning on having someone else train them in terms of game retrieval, flushing birds, what have you? What's the plan there?

You say you want to rescue, but you can't start a good gun dog off at three or four years of age. They have to start as puppies, so I'd be very worried about a rescue failing those qualifications. I don't know this for certain, I don't have a gun dog, but my understanding is you start from square one because lacking things like a soft mouth or lack of fear of noise will basically ruin them for any hunting sport.

A puppy is a 24/7 game. You don't train a puppy two hours a day. You might actively train them in terms of commands for that amount of time, which I assume is what you mean. But you're with them all day, every day, until they reach some level of maturity that differs by breed.

A lab would suit for hunting, kind of, but a Bernese is a pulling dog...totally out of line with what you're looking for.

Almost no rescue will adopt a dog that isn't a house dog. You can lie to them, that's an option, but leaving a dog outside all day and all night is irresponsible. It can be outside the majority of the time, but it has to be a house dog. It has to have its primary place in the home. If you're not willing to do that, and you're not getting a rescue. It is not fair to the dog to be outside all day and all night. There are also any number of accidents and random circumstances that can really compromise their health and safety.

In other words, you don't seem to know what you want yet. This is a hot mess of conflicting desires. The closest I can come is a Brittany Spaniel which seems very close to what you want, but outright defies some of your stated desires, cannot live outside full time, must be trained as a puppy, and really won't be a rescue dog in most circumstances. You have to buy one outright as they don't often end up in rescues.

You want the magical dog that is super easy and causes no trouble and does everything you want, which just isn't possible. I think you need to take more time and think about what the priorities are before you adopt or purchase. There are serious trade-offs with every breed, even in a mixed-breed situation.