Nah, I don't think even in-universe ONE intends for Saitama to be literally unbeatable. ONE has said himself that the point of Saitama is that, unlike most Shonen MC's who need to grow throughout the story, Saitama's power is already what he should have at the end of the series. If you put current Goku back in the OG Dragon Ball or current Naruto back in the OG Naruto, they'd also one shot anything there. Saitama has endgame power at the start of the series. That's how he parodies Shonen anime, not just "haha he big funny he one shot people". As for the whole gag thing...honestly at best, I could only see it being a thing where ONE might have originally intended for Saitama to be a practically omnipotent gag character, but as the story progresses, we see many times that Saitama is actually a serious character with his own character arc. Saitama's character arc is literally about his own pseudo-apathy and depression caused by his overwhelming strength, that's not what you'd see in a gag character.
Take the Boros fight for instance. Numerous times in the battle, Saitama is surprised and even blatantly impressed by Boros, not only calling him strong on multiple occasions to Boros, but also referring to him as a strong opponent afterwards. When he gets kicked to the moon in the manga version, he even says that it's almost like a real fight. We know that Boros is a parallel to Saitama. Someone who became so strong in search of the thrill of combat that he became too strong. So much so that no one was a worthy opponent for him. We even have implications that Meteoric Burst temporarily breaks Boros' limiter, and in the OPM Compus (which I don't think is inaccurate so much as it has a single big mistranslation), it's even said that MB Boros "sort of clobbered" Saitama. And lastly, when Saitama walks away from Boros with his eyes shaded, his head downwards, and Boros weakly calling out his name with his dying breath...like, who thinks that was supposed to be funny? The reason why Saitama looks like that is because, unlike Boros who achieved his dream of a challenging fight against a powerful foe, Saitama still was unable to really try, he was still not challenged. He could've ended the fight whenever he wanted to and didn't take seemingly any actual damage (unless you trust the cover that states he took damage from one of Boros' attacks). Boros was in Saitama's general league, but he still wasn't close to Saitama's level. And naturally, the fact that Saitama encountered someone this strong, someone who had gone through the same boredom as him, but still couldn't be provided an actual challenge, only furthered Saitama's depression, as it likely seemed then and there that he would truly never find a rival of his own.
We see more of this in the Hero Hunter arc of course, with Saitama's talk to King. Saitama believes he has reached the pinnacle. There is nothing left for him anymore, there is no more room for him to grow. The conversation is ended off on a comedic note and hasn't been addressed very much since then, but Saitama's current character arc is very real, and will be explored more in the future.
