So, something I think might be missing from this conversation is who is in control of the character. What do I mean by that? Well, let’s look at a simple attempt to persuade a guard to let the party past, using mundane means. The player describes what their character does to try to persuade the guard, maybe by speaking in character, or maybe in third person, saying “my character tries to politely explain to the guard why it’s important to let us pass.” Then the DM decides if that action has a chance of succeeding at the goal or not, if a check is needed to determine its success or not, and if so, what check (in this case, probably Charisma + Persuasion). The DM still has agency here, she has the power to say that this guard simply cannot be swayed by polite requests, she’s a woman of action, and only action will change her mind.
Now, what if the player casts charm person on the guard? Now the DM no longer has a say in whether or not that works. The rules state exactly how the spell functions, whether the DM thinks this is something the guard “would do” or not. Now, yes, the DM is the final arbiter of the rules and it is technically within their power to say the spell doesn’t work that way in this instance. But generally speaking, the purpose of codifying the effects of the spell is to put the power in the player’s hands to say “here’s how this action is going to be resolved.” Mind control spells remove the subject’s agency by removing (or at least reducing) the ability of the person controlling the character to influence the outcome.
Now apply this to a PvP action. When Harold tries to persuade Jessica’s character to go along with his character’s plan, and the DM tells Harold to make a Charisma + Persuasion check, Jessica’s character doesn’t really have agency in the situation, because the person in control of the character (Jessica) didn’t get a say in how that character reacts. She didn’t get to decide that her character is a woman of action who won’t be swayed by words alone, the DM just went ahead and decided that, yes, this attempt to persuade her character has a chance of success and failure, and that Charisma + Persuasion is the most appropriate way to resolve it. It may not represent mind control in the fiction, but it feels like mind control to Jessica, because, like mind control, it removes her ability to decide how her character reacts. From the perspective of the person who is in control of the character, it is functionally alike to a mind control spell, in a way that it would not be alike to a mind control spell if the target was an NPC.
This is why I have players resolve any PvP actions taken against their character. In this situation, they are in control of the subject of a player-initiated action. That should function the same way it does when I’m in control of the subject of a player-initiated action.