No panel him getting back up and active if next several pages it never shown up again. Just Drake and Hawkins. If he was alive, then doesn't make sense to quit mission or leave as his personality doesn't look to be the type for that.
Well that's the shit that Toei was supposed to ask Oda right?
The right was entirely inconclusive in the manga. You have no proof that page one actually got beaten. Neither drake or hakwins even say that Page one got beaten even when they find Sanji, Drake only cares about The germa shit and never says anything like "You defeated page one"
A million things could've happened. He could've been called away on another mission or he got punished like killer for letting Sanji escape or whatever other shit.
Toei doesn't have the right to decide a character has been defeated or not when Oda himself hasn't told them he was defeated.
Obviously the anime saying Sanji ran away is still not canon since that's also not confirmed in the manga but its also not confirmed that he beat page one so none of it matters. It's not even confirmed that he made page one bleed even once.
At Least the fight was well animated so the there's that