Can somebody recommend good vegetarian food which gives you on a long-term scale (one day, 1.500 hm difference in altitude, or multiple days) enough energy / calories, but does not affect your stomach during an exhausting hiking day?
What about tofu? I would prefer low sugar and low carbs.
Aside from alpinism/mountaineering, there are many scenarios where people might want a lot of food that doesn't weigh too much. Long journeys like through-hikes, mountaineering, or voyage by train or ship all have similar requirements so I'll try to provide an answer that works for all of them.
For lightweight food that lasts, the primary objective is to select dry food, for two main reasons.
Fats (lipids) are highly desirable in these cases. We might intuitively think of fat as being wet because oils are a liquid at room temperature and fat content is often connected to the perceived moistness of food, but it can really be considered as dry because fats are very lightweight (for a given amount of energy) and don't contribute to decay the same way that water content does.
So to finally answer your question, you'll want to select foods that either start with a low water content or are suitable for dehydration to reduce the water content.
Of course, some of this food is going to take a bit of work to make it palatable. You'll need to work out a plan on how you'll obtain water, and depending on your specific activity, you may also need a way of preparing food to rehydrate it. For alpinism and long hikes, making a stew is one of the easiest ways to rehydrate dried foods. For unsupported journeys in the outdoors, you'll definitely want a water purification system that allows you to use the water you collect along the way. Any water you can get this way is water you don't need to pack.
You mentioned tofu in your question, but tofu is not a very good choice. Tofu is only about 1.1 kcal per gram, and you really want to be selecting foods that offer at least 3.0 kcal per gram (as a rough benchmark).
Couscous and peanut butter are the most energy-dense vegan foods by both weight & volume that don't require cooking (excepting sugar, which is more energy dense but doesn't satisfy hunger).
Consider the following items:
Less-dense vegan items (some that require adding boiling water):
And if you want fresh food, then you can sprout lentils by soaking them in an old peanut butter jar after you reach camp, draining & rinsing them in the morning, then letting them sprout in a sprouting bag hanging off your pack during the day.
You could also make chapati (flat bread) with flour, sugar, salt, water, oil. Flour & Sugar are more energy-dense than couscous, but this requires quite a sustained fire that will take much longer and use much more fuel (likely unavailable in an alpine environment) than the above options that can be rehydrated with cold water or just-boiled water.
When I (vegan) go trekking, this is usually what I bring per day (I buy these items in bulk, so I just measure them out into gallon ziplock bags by the handful. For reference, 6x handfuls of couscous is 200mL by volume):
If I'm only going for 2 days, I'll just double the above list. If I'm going for longer treks (eg longer than a week), then I'll add the occasional less-dense items (eg flour tortillas) to add some variety. After 3 days, it can be hard to throw down couscous & lentils twice-per-day.
I'll also have
You many not need that much food, but I do. I know a lot of people who plan on just having a snickers bar for lunch when they go trekking, and they expect to come off the trail a few kilos lighter than they entered. Personally, I have hardly any fat on my body, and I have a crazy high metabolism, so I pack way more calories per day than most people. YMMV.
Dried nuts are a particularly dense source of calories and nutrients, including as spreads like in peanut butter. Tofu would be too watery, as commented by Zanna. Tempeh (fermented tofu) is a plausible middle-ground option. Lentils or beans are also good options with relatively few calories compared to more standard offerings like crackers. Also consider dried fruit, but that is higher in sugar.
