That’s absurd. He is left of center in the USA by a wide margin. Saying he’s not of the left or not a leftist is quite the goalpost, especially considering his achievements such as getting statewide free lunch programs at schools.
Socialist does not mean the same thing as leftist, and isn’t the criteria to be considered “of the left.”
Maybe I'm wrong, but I consider "leftist" to mean something like "a collection of positions rooted in criticism of capitalism." Socialism would be one such worldview (a subset or example of leftism), but so would communism, some forms of anarchism, and more. "Free school lunches for everyone" should probably be considered a leftist position as it undermines the profit incentive of recouping the cost of that lunch, whether he presents that as a leftist thing (which I can see causing some political blowback that he may try to avoid in the name of progressing this kind of legislation) or not. I haven't had time to do any other research on this guy or his other positions. If he supports a lot of legislation in this vein, then maybe it's okay to call him a leftist.
Regarding the profit incentive: providing free school lunches or medical/ hygiene supplies does not hurt profits. As the meals/supplies will still have to be sourced from the market, it probably will now be a few big contacts with big suppliers that will cover entire school districts.
The costs of these contracts will be a public burden unless they implemented a specific focus tax to pay for it, so it will come out of various broad tax pools.
This means everyone pays a little bit so every kid has something to eat. Even if you don't have any kids or if your kid gets homemade lunch packs. This is where the "social" aspect comes in.
Other countries, many of them European, actually go a step in the other direction: if you do not have kids, you actually pay a premium on your income tax. And that is generally accepted, because for society to live on, obviously kids are necessary. And if you don't support society by raising kids, you at least help cover some of the associated costs. These premiums are explicitly used to fund kindergartens, schools etc..
An often valid capitalist criticism of public large contracts on infrastructure such as this is that the public offices tend to be notoriously bad negotiators, accepting worse deals than private companies would. This is because there's little to no incentive for them to reach good terms. It also makes the process more vulnerable to corruption and politicking on a grander scale. These are not guaranteed to happen, good governance can definitely avoid this. But public governance simply isn't that great to begin with in many areas.
Leftism isn’t about being anti-capitalist, though the two can and do overlap quite a bit. Left wing politics is more about what they support as opposed to being against something: pro-human rights. Pro-equality and equity. Pro-education. Pro-healthcare. Pro-environment. Walz is pro all of those things, and his track record exemplifies it.
It may seem like splitting hairs, but the distinction is important. It’s the right wing that only exists in opposition. Their only platform is what they are against.
Compared to many of his Democratic colleagues, he leans much farther left than most. That’s why it’s odd to say he’s not of the left. He is a capitalist who owns not a single stock, bond, real estate, and he doesn’t take money for speaking or have book deals. He’s a lefty capitalist, which is pretty much a diamond in the rough.