

4.5 billion divided by 1 billion is 4.5. You’re off by an order of magnitude.
Also, there is a lot of stuff we can see within 47 light years. Stumbling across a planet that was ejected from our solar system is highly improbable, but even less so is that planet being captured by another star and having a stable orbit. Not impossible, mind you, but the lottery is a safer bet.
We didn’t know this before we had the James Webb telescope. Now we have enough resolution to read the name tags.