I don't really like this discussion from either perspective.
Mostly because there isn't a single "correct" version of Superman.
This is a character that has been reinvented over and over since 1939. His politics shift not only due to the era, but also due to the current writer's sensibilities and beliefs.
If you want to refer to Jerry Siegel and Joe Shuster's original intentions, Superman was an opposite reflection of the Nazi Aryan ideal. They were Jewish and wanted to use that ideal against the principles of nazism. Superman looked the part—tall and muscular with chiseled features. But he saved the weak and helpless. He was compassionate and just.
"Truth, justice, and the American way" was a phrase created for the first television show. In that era, "the American way" was understood as wartime patriotism and American ideals of freedom and family—but all in the context of that opposite reflection of nazism.
"The American way" was basically understood as "Hey, at least we're not fucking Nazis."
I don't think modern labels of conservative or liberal would fit that version of Superman. But if you were to shoehorn it, there is only one group currently harboring nazis and fascists, and it isn't on the Left.
There is one version of Superman that was coded more conservative.
Frank Miller, famous libertarian and misguided curmudgeon, had a version of Superman in The Dark Knight Returns who was basically a pawn of the US Government. A supercop for Ronald Reagan. He was depicted as more of a nationalist than a patriot. His "American way" was based on "might makes right." America is the good guy in every possible scenario.
I'm pretty sure Frank was mocking the Superman archetype. Satirizing how America would *actually* use a superpowered being. Basically, the only conservative version of Superman was coded as a villain or nemesis for the anti-authoritarian Batman.
If you read The Dark Knight Returns and feel Superman is depicted as a positive conservative figure, you probably also think Homelander is the heroic protagonist of The Boys.
Superman's politics cannot be easily condensed into a single ideology. You'd have to analyze each writer and their intentions individually. But the persistent characteristics of Superman over the years would definitely lean him toward progressive ideals.
He was a fantasy created by two marginalized Jews who were watching their people get slaughtered by fascism. A figure that could use his immense power to protect those who cannot protect themselves.
If that version of Superman existed in real life today, I suspect he'd be visiting a prison in El Salvador to facilitate a prisoner release with laser eyes on standby.
