My proposal is that SNAP only covers food and drink items that are 2 ingredients or less.
All fresh meats (beef, chicken, pork, etc) or frozen meat so long as it's plain
All fresh or frozen vegetables
All fresh or frozen fruit
Flour, sugar, butter, milk, eggs, single ingredient Seasonings and salt
Plain water, or unflavored sparkling water, tea bags, coffee grounds, milk.
Everything else is not purchasable. The reason for two ingredients instead of one is it allows items like butter which may be salted, or yogurt which may have bacterial cultures as an ingredient.
Unfortunately, this would cut some decent items like sausage, bacon, deli meat, bread, condiments, and some other items but I would consider it a necessary evil. Plus plain meats are way cheaper anyway and any luxury item they can purchase on their own dime.
This would avoid the problem of trying to decide what's healthy or not while completely excluding any and all processed foods including soda and candy.
You can compose a whole diet from only items made up of two ingredients, you can bake your own cookies and desserts if you want a treat, but you cannot buy processed foods or sugary drinks.
Individuals can decide for themselves what their diet should look like, and what they consider healthy. The government doesn't have a good track record for deciding this, and some may have special dietary needs they need to account for anyway. So this should be a decent compromise.
A bunch of meat and cheese and eggs? Fine. Rice and beans and a little bit of fish? Whatever. Vegetarian or plant-based? Have at it. But no processed foods.
Would this necessarily force people to be healthy? Probably not because they could just buy sugar dump it in water and guzzle that down. But I'm betting it would help because most would be too lazy to make cookies or cake and what they make wouldn't be as addicting and easy to access as doritos and snack cakes.
Main point. If you want pop tarts or candy or soda or whatever else get a fucking job and buy it yourself.