Otherwise, you would have to contend with the fact that "real time" does not exist at all, as information about any event has to necessarily take time to travel to reach you.
So no "real time" coverage of anything -- the information always takes time to travel the distance.
What is not a correct understanding of how time works is claiming that it happened some thousands of years ago. No, from our reference frame it happened now. It is meaningless to say that it happened thousands of years ago because it happened thousands of years ago in some other, arbitrary reference frame.
It didn’t happen in real time, but they did observe in it real time.
One is a measurement of the event and one is a measurement of when the photons reached us.
I point my telescope at a planet four light years away (I have super advanced telescope that can see these details), and use a worm-hole or other plot device to teleport instantly to that spot. Where do I arrive -- at what I observed, or at some point in empty space because I've just arrived at where that planet was four years ago?
If the former, I must somehow have traveled back in time by four years to arrive at the spot I had observed.
If the latter, I suppose we could instead say our destination is where we calculate the planet will be four years from now. Except that my travel time was instantaneous, so again either I've arrived too early and need to wait around for four years, or I jumped 4 years into the future (at which point that's not really FTL travel, just kind of stepping outside of time into some nether state for four years).
This doesn't make sense. If you have a wormhole teleporter, and teleport to where that 4ly-away planet is in your observation, it won't be there, since you saw it 4 years ago and it's moved. This seems fairly obvious.
Now, if you observe its motion and predict where it's traveled in the 4 years between your observation (now) and when the photons you saw started from that planet (4y ago, relative to your current position in spacetime), and set your wormhole teleporter to take you there instead, it should take you to the planet's current position. (Hopefully your calculations were accurate and you don't teleport into the planet...) I don't see why you think you'd arrive too early, or jump into the future. Your friend who stays behind would need to wait 4 years to see you arrive at the planet in your super-telescope, but that's just because it takes light that long to arrive.
I don't see how this particular thought experiment necessitates time travel.
Technically, one can argue that "real time" is relative to the time frame in which we observe something, but that's not how we generally use "real time", but rather we use it to define an event that is observed at the same moment (or very close to) the moment in which it occurs, such as a match broadcast live on TV (though there is some delay).
Due to this relative motion we will see different ordering of events at different locations, despite both being at rest relative to the CMW background, so we can’t really say there is a global timeline.
The thing is that the CMW background isn’t global, we don’t see the same background as a distant observer. CMW photons that are passing us now will take time to reach a distant observer, and vice versa.