Very noble diet/ethos for many reasons, but it is not optimized for nutrition, it's optimized for other goals.
Also, EPA/DHA is really powerful stuff.
Some diets, including a standard american diet but especially exclusionary diets like vegan, vegetarian, keto, carnivore/paleo diets can have major nutrient gaps. Those types of diets require careful planning of meals and/or supplementation to address gaps.
Magnesium isn't hard to get. Vitamin D and EPA/DHA are easy to get if you eat animal foods (esp fatty fish, liver, cheese and eggs).
Probiotics is a vague category and hasn't been shown to be necessary in a diet. Medical science understands so little about the gut-biome that you should be extremely suspicious of anyone claiming to be an expert. The advice usually boils down to general platitudes like,"Fermented foods and fiber feed our gut bacteria and is good for overall gut health." without defining what any of that means or how it works. I guess other animals/omnivores that don't eat fermented foods or fiber must really be undercutting their lifespan potential.
https://www.reddit.com/r/ScientificNutrition/comments/adfowt...
It's a shame from a nutrition standpoint, but veganism is NOT a diet for optimal nutrition. It is an interesting diet from an ethics standpoint, I grant them that. And despite the long-term wasting away effects, veganism is superior to a standard american diet loaded with sugar, heavily processed carbs and vegetable/seed oils.
Michael Greger, MD does: How Not to Die [0]. Basically, to save you from reading the book, go vegan. He has a great cookbook too based on the advice in the book [1]. His nutritionfacts.org site in general is an excellent, science/fact-based resource.
[0] https://nutritionfacts.org/book/
[1] https://nutritionfacts.org/cookbook/