Geno is in this weird state where more than pretty much every other character he's defined just as much, if not more so, by the requests for him to be in Smash than anything about the character himself. Seriously, you can't really talk about Super Mario RPG without mentioning or having someone bring up "Mr.Not In Smash" himself as such. He's pretty much become the face of the game somehow, even if you know absolutely nothing about Mario RPG, you know it's the game he's from. This isn't anything new by the way, while this has certainly become more prevalent over the years I remember even back in the first half of the 2010's, way before Geno ever officially got acknowledged, it felt like people always mentioned him as the "guy people really wanted in Brawl for some reason" when talking about SMRPG.
Pretty much the only character I can think of who fits a similar situation is Ridley, who's dismissal for being "Too Big" reached meme status to the point of being his tagline. Waluigi gets close but he's a giant meme regardless of the Smash situation surrounding him, it's just a large part of it. Every Smash Cycle certainly gets those characters as well, I'd argue Mewtwo in Smash 4, you couldn't talk about Banjo for a straight year after Ultimate got announced without someone mentioning Smash.
Of course Geno's reputation as the guy who didn't get in Brawl persisted but he really wasn't as popular in the Smash 4 days, though I'd argue that's less him being less popular than before and more just the community being bigger and a larger possible selection of characters compared to Brawl. Then the mii costume happened, people realized he actually has a shot after losing faith, then Ultimate happened, the two most persistent "never-evers" got in with Ridley and K.Rool, other fan requests and characters that got acknowledged with the Smash 4 DLC like Inkling, Chrom, Isabelle, Dark Samus, Simon, and all the veterans came back, and people start thinking "Hmmm, there is this character they went out of their way to acknowledge being highly requested last game, and straight up said they wanted to have them in Brawl yet gave no reason why they didn't make it", yet nothing happened and by this point the reputation has completely stuck and grown even more, especially after Banjo gets in, where he's pretty much the one big "never-ever" remaining besides maybe Waluigi.
I don't want to imply Geno is a bandwagon pick (mostly because I don't really see anything wrong with that anyway, isn't the entire point of Smash to introduce people to new characters and games?) but a big part of his appeal and popularity in Smash ironically comes from the fact he hasn't made it in in the first place.