Although you are vulnerable to Assassinate only if you are still surprised when that attack hits, there are many possible causes of being unable to move or act. Therefore, 'unable to move/act' is not the same thing as 'surprised'.
"If you’re surprised, you can’t move or take an action". The implication of this is that if you
can move or take an action then you are
not surprised.
Also, cause goes before effect, not the other way round. 'Surprise', among other things(!), causes 'unable to move/act'; 'unable to move/act' does not cause 'surprised'; nor is it equal to 'surprised'.
No. Not noticing a threat causes you to be unable to move or take actions until the end of your first turn. Which of these would you call "being surprised"?
You are saying that.
But the rules do not.
The rules say exactly this: "If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a reaction until that turn ends." Which is exactly what I said. The thing that happens if a creature is surprised (being unable to act or move), ceases to happen at the end of its turn.
If you speed, you get a fine. But the moment you pay that fine has absolutely nothing to do with when (or if) you stop speeding.
If you are surprised, you cannot move/act on your first turn, but the timing of that penalty has nothing to do with when you stop being surprised.
This mechanical penalty, as you conceive it, seems rather disassociated from the fictional conditions it is supposed to simulate. Are we to imagine our characters waiting for their time in the penalty box to be up because they have transgressed against the commandment, "Thou shalt notice a threat"?
You are surprised for as long as you don't notice a threat.
How long do you think the "start of the encounter" lasts? That's the period of time in which you are surprised if you don't notice a threat.
Your reaction speed measures how soon you act, when you notice that there is something to react to, it doesn't inform you that there is a threat.
No, of course not. That would be silly. Is that what you think I've been saying?
If so, you must be confused, so allow me to explain without any reference to the word "surprise". Your reaction speed (i.e. your initiative) measures not only how quickly the actions you take are resolved, but also how quickly you recover from being unable to move or act due to having not noticed a threat. For example, a wizard who has thus recovered may cast Shield in response to an attack that will hit him, regardless of whether the attacker had previously been noticed, whereas a wizard who hasn't yet recovered could not cast his spell.
Since it says that a creature who doesn't notice a threat is surprised, it kinda does!
A creature who doesn't notice a threat is not surprised at any time other than the start of the encounter. That's when it says the creature is surprised.