That's just it, nothing has happened so nothing is wonky. Surprised to not surprised is not something happening in the fiction. The character doesn't actually act. They don't get an action or a bonus action.
The only difference is that the Assassin won't auto-crit. That's it. They still get advantage and sneak attack damage.
That's what's wonky. First, "surprised" to "not surprised" sounds like it should mean something in fiction. Second, a "natural language" reading of the situation is nonsensical, since there is no reason for a character that hasn't been attacked by an attack they aren't aware of to be surprised in the first place. Third, an Assassin waiting for an auto-crit would be a circumstance for which the assassin would just have the target re-roll initiative until the assassin won (assuming that the player knew when the target was "surprised" and it was "not surprised").
Wonky!
The Monk can literally catch an arrow they were unaware of if they win initiative. Even if the Assassin hits. This happens in stories about kung fu Monks.
My point was that initiative doesn't represent the monk's preternatural awareness. In 5e, that's baked into the monk's AC.
Wait, are you implying that winning initiative makes you aware of attacks that haven't happened yet? That's a new one to me.
The rules say that you are allowed to have a reaction to an attack as it is happening if you have won initiative. That is all that winning initiative while surprised does.
But if a creature is surprised and no attack comes...what were they surprised by? How did they stop being surprised?
Order of Operations:
1 - Assassin: "I shoot my bow at the unaware guard!"
2 - DM: "Okay, the guard is surprised. Roll initiative."
3 - Init is rolled. Guard wins.
4 - DM: "Okay, the guard is not surprised anymore because of reasons. Your turn."
5 - Assassin: "Okay, I don't shoot the guard." / "...I ready an action to shoot the guard when she IS surprised."
6 - DM: "Uhh...okay, no combat happens, and the guard continues on its patrol, still unaware of you. What do you do?"
7 - Assassin: "I shoot my bow at the unaware guard!"
8 - ...etc?