Well, Octavian was a genius of the propaganda... I really do not think anyone else would have been able to sell the success of Antony's plan (that was not a sea battle but Antony's fleet was escaping from the siege of Agrippa with all their gold (main reason for which the major battle was the one on sea and not the one of land) as fleeing from the battlefield abandoning his men. And who Antony was able to escape when one of his most trusted men defected the prevoius evening, revealing Antony's battleplan to Agrippa and Octavian is nothing short of a miracle (sure Antony was smart enough to not say the true reason for which he had chosen to give the priority to the sea escape instead of the land battle, in which he was better, aka who they need to takew with them a lot of gold)
Octavian was a genius of politics, not just propaganda, but that’s beside the point. Antony repeatedly tried to break out by land in August, and he failed, that’s why people started defecting to join Octavian. Breaking out by sea wasn’t even his original plan, he wanted to lure Octavian’s fleet into the strait, but that failed, so he decided to take flight as his last resort, since he knew that by doing so he’d leave the land army to its fate, and he would never manage to get most of the fleet out. Considering he started the campaign with superiority in resources, men and ships, I wouldn’t call losing most of his troops, 430 ships out of 500, and all the pull he had on his allies a victory or even a miracle. His last, desperate plan worked and he got out with the gold, so what? It’s not like he put it to proper use anyway. Whatever Octavian’s version of the tale was, nobody can objectively deny that Antony lost at Actium. Regarding his military talents, to each his own, but I personally believe Antony was the reckless version of Pompey, both grossly overrated in their days, both losing to a superior foe despite being greatly advantaged.