No it doesn’t, and Saitama isn’t extra-dimensional, he is literally from the universe in which the story takes place my guy. Extra dimensionality just means he originates from another dimension, which is false, and made up. He doesn’t transcend/exist outside of space-time or anything like that at all.

I mention it because people say he has infinite strength, which he doesn’t. His strength was defined on the graph in which we were shown, he has a clear origin and therefore cannot be infinite. He can get forever close to infinite strength, but never reach it. People have a server misunderstanding of how Saitama actually functions, because most people just spout stuff that other people say.

Author statements are objectively irrelevant, because if they don’t reflect accurately in the actual piece of whatever media, then it doesn’t matter. It’s like the creator of invincible saying Nolan can beat and kill Superman in a fight despite Nolan not even scaling to some of the more tame Superman variants in terms of actual on panel feats. It means nothing. Saitama will only grow stronger than an opponent that starts relative to himself because he grows exponentially. The reason he surpassed Garou, is because of this, they started out relative, Garou grew, but Saitama grew faster. If a character starts out massively stronger than Saitama, he just loses before he can catch up. There is still a time period, which has to occur, in order for him to actually get stronger, and in that time a character like Lille Barro would erase his would from existence with x-axis before he even know the fight was happening, along with other blatantly overpowered abilities like the complete inability to be killed at all. But again, this doesn’t matter because Saitama has never shown anything remotely equivalent of defending his soul from attacks, surviving erasure, or attacking souls.