It rather depends on what you are using to do the automation, but basically it is 2).
If you are using Smart Lighting in the Classic mobile app you can only specify one category of device as the trigger, such as a switch or motion sensor. You can specify multiple devices in the same category as the trigger but ANY of them will trigger the automation. You can add conditions such as another switch being on but these are only checked at the time the trigger event occurs. So it is a bit like your 2) except you’d need two automations. One for the living room light turning on when the TV plug is already on, and one for the TV plug turning on when the living room light was already on.
More generally, if the application you use for the automations lets you specify two triggers that must both be met it is likely to be more like your 2). The second light or plug being turned on while the other one is already on will trigger the action.
Your 1) is arguably more complicated that it seems. What does ‘the same time’ actually mean? Exactly the same time to the millisecond? Within a second? It could certainly be done but it isn’t something that is likely to happen as a default. It is something you’d have to specifically request or program.
You have already ruled out 3) by yourself and I think you are right to do so. It will usually be the light or plug being turned on that wakes up the application handling the automations so it can see if it needs to do anything. Otherwise it would need to be constantly checking the status of the plug and light to see if it needs to do anything. That is possible but again not something that would be default behaviour.
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