If you're unaware of attackers you're surprised. If you're surprised you don't get to act, move or react until your first turn is finished.
If an assassin initiated combat, but the party concluded the battle halfway through round one. It's concluded. I suppose the upstaged assassin could resheathe their half drawn dagger, or what have you that started the battle. A bit of sleight of hand and no one apart from their friends might ever know they started it.
In real world, surprise is so powerful because sudden extreme aggressiveness forces a rapid change in mindset. But after an initial attack, no one will be in a relaxed frame of mind. I think the RAW supports this narrative quite beautifully, actually.
Now, if Calm Emotions were cast, or some clever acting were done - against a higher DC, perhaps skilled PCs could pull it off again in short order? Yeah, I'd let players get creative.
Regarding Charm Person to end the battle... It depends on how the fight started. If the assassin drew an unseen dagger but the Enchanter charmed the foe - before the foe had their turn, well, the foe's only enemy would be a 'trusted friend and ally', so they'd still be in a relaxed unaware state. Put yourself in the mind of out NPC, that can help adjudicate these things.
If, however, the foe had ended their turn before being charmed, too slow! They would have picked up on the tenseness and become alert. There are uncommon weapons of warning, Dex ASI's and the Alert feat in the game for a reason. Maybe delay SS until shoring up initiative?