I presume you can guess the broad outline of the question from the details of my answer. ;-)
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I am not bothering to narrate the fact that the single biggest economic difference you can make is between eating in restaurants vs. cooking for yourself: anywhere in Europe, NOT BUYING restaurant food (and not buying chocolate bars, etc., "convenience food") is much more significant than the slight difference in price between two competing items at the grocery store.
This disclaimer may be the real advice you need, and it may not be: some people don't realize that if they want to save money (on food, etc.) THE MAIN OPPORTUNITY they have to do so is refusing to meet friends in restaurants, or even refusing to buy convenience food while waiting for a bus after work (or after school, etc.). Making your own sandwich is always cheaper than paying someone else to make a sandwich for you —but in Europe, this difference is dramatic (whereas in China, many people eat in restaurants three meals per day, because the difference in price is very slight).
I have never lived in Sweden, but my experience is that 90% of the groceries available in France are also available in Germany and Greece —i.e., the options are overlapping and similar throughout the E.U. bloc (but, admittedly, Spain would be better for fruit and vegetables than Sweden, at opposite ends of the E.U. climate spectrum, and I aside you rely on many things imported from Spain, as even the British do).
The fundamental strategic decision you need to make is this:
Will you get protein from a powder, or from beans, peas and lentils?
Canada produces vegan protein powder: the cheapest I can get costs less than 15 Euros per kg —more expensive brands (THAT ARE NOT BETTER, IMHO) cost about 27 Euros per kg.
If you're buying protein powder, everything else in your vegan diet is easy, both economically and nutritionally.
If you have vegan protein powder and a multivitamin pill every day, the rest of your diet can be cereal and soymilk, and you'll be fine —although if you want to make the effort to eat salad every day, go right ahead (although you know very well this will cost you more time and money).
The question becomes somewhat more interesting if/when you decide NOT to rely on protein powder (and, again, economy is a factor here, as you've posed the question in this way).
What is your major, daily source of protein going to be?
White rice with yellow lentils? Canned peas? Beans that you buy dry, and prepare in a pressure cooker?
Whatever the choice you make, everything else in your diet is going to revolve around this decision: if the "backbone" of your diet is white rice with (Brazilian) black beans at every meal, then the other vegetables / side dishes that accompany this will be influenced by the procedure of preparing the rice and beans.
You're not going to combine black beans with bread and strawberry jam. You could, but you won't.
The economic problem is just failing to think these things through: if you eat "impossible burger" style processed food as your main source of protein, it will massively increase your costs over any of the options narrated above. Obviously, if you try to eat a diet based on tropical fruit (in Europe) it would massively inflate your costs. The first can happen accidentally, as people just start buying packaged and processed main courses for convenience without thinking it through; the latter (a mango based diet, etc.) never happens accidentally (it happens ideologically).
All of Europe has high quality lentils available. Canada does not. All of Europe has high quality canned peas available. Canada does not. This is hardly an exhaustive list: it would be really depressing to get into the details of how abominably poor the quality of food is in Canada. Lettuce is bad here. Basically all fruit and vegetables are bad here. Everything here is worse than Europe AND worse than Asia (e.g., worse than Taiwan, not just worse than Thailand).
In any given social context, there are limits to how much money you can save on food, without changing your social context: if you really want to save money beyond what I've described above, refusing to watch movies, refusing to drink alcohol, or moving into an apartment with cheaper rent (etc.) will all be more significant that the difference between (e.g.) the cost of lentils and the cost of black beans —or the cost of protein powder and any/all beans.
In the 21st century, food is obsolete: all you need to live is contained in the vitamin pill, the protein powder, and then practically anything (such as cereal and soymilk) to make up your remaining "macros" (i.e., the sheer number of calories you'd need to live). We all live in the shadow of this obsolescence, not wanting to face up to its implications, because this entails that our whole culture of cuisine is obsolete, and a large portion of our notion of happiness (and enjoyment) is obsolete, too.
