...yeah. That's all this comes down to. There's no slow motion replay answer to this.
But when it was applied to a genre and defined as such, it was Superman that was unanimously credited as the first. Alan Moore, a guy who knows comics history, has repeatedly identified Superman as the first superhero. He did that most recently in an essay "Buster Brown at the Barricades". Literally every major comics professional said that superheroes began with Superman.
Everyone agree that the superhero genre has a "Before Superman and Action Comics #1" and "After Superman and Action Comics #1". America celebrates July 4, 1776 as Independence Day, and obviously there's an America before that day and an America after. But people drew a line in the sand and said "this is where it starts".
Separating wheat from the chaff isn't goofy. Identifying the superhero genre as a distinct specific thing from earlier action adventure genres isn't goofy.
If we keep going further and further back, the definition loses meaning and purpose, it stops making sense. If you want to make the case that labels are meaningless and trite, then that's fine but anybody who wants to call Hercules "the first superhero" is still indulging in labels only with far less justification. Calling Hercules the first superhero tells us more about people today (and Americans today especially) than it does about Hercules and how people in the Ancient World saw him.
The word can be traced back to Friedrich Nietzsche and his concept of the Ubermensch and was originally translated as "The Superman" (which is avoided these days by philosophers and others who use "The Overman"). That word concept you cite "a public figure of great talents or accomplishments" was what Nietzsche meant. To him Napoleon Bonaparte was the Ubermensch (although for him, the word Ubermensch had a philosophical distinction that it didn't have). In the 19th Century you also had people going on about "Great Man of History" and so on.
Siegel and Shuster inspired by that concept did a science fiction story called "Reign of the Superman" in the mid-30s that was about a mad scientist. But then they retooled the concept and when they did the comic, they made Superman into a crime fighter with great powers who poses as a civilian and wears a bright costume, and poses as a champion and defender of the people. So again, Siegel and Shuster redefined and reapplied the meaning of the word Superhero with Superman, and created our current definition of it. Newsflash to people...words and their meanings change. Over time and history. Culture is a real living thing. And that is why slow-motion replay approaches to "what came first" is nonsensical on a fundamental level.
Batman does fight superpowered villains in the Golden Age and in modern times.
Obviously the genre evolved and changed over time. The point is that when Superman first arrived and in the first decade defined and created the genre, those were the foundational elements of the soup. In any genre, over time you have changes, additions and alterations within the genre as time passes. "The Great Train Robbery" is the first western movie made in the 1900s, but obviously the fact that there are westerns that do not have train robberies made later doesn't mean "The Great Train Robbery" isn't the first western.The Fantastic Four...
Nope. The concept of the supervillain is older than the superhero. You have examples that can go as far back as you want. The 19th Century had many adventure novels with monsters and mad scientists and madmen like Frankenstein, Dracula, Captain Nemo from 20,000 Leagues Under the Sea, Moriarty and in the early 20th Century you had Fu Manchu, you had Dr. Mabuse and others.
Chester Gould's Dick Tracy was famous for its distinctive and iconic gangster villains and most comic book rogues, especially Batman rogues, were inspired by Dick Tracy albeit with the difference...Chester Gould killed of his villains and most of his well known rogues were one-shot characters who died, often brutally in encounters but people remembered those rogues to create serial incarnations of it.