... If you made the round trip to Alpha Centauri and back at virtually the SOL, hundreds if not thousands of years will have passed by the time you return to Earth.
If you travel at the SOL, time actually stops.
Although this could be said to be a form of time travel, its not time travel in the sense that you can go backwards into the past or forwards to the future.
Why not? That last sentence hardly makes sense. If I can get in a box for a minute of my time and come out a week later compared to everyone else, then I have traveled forwards into the future.
Which seems to be a little at odds with your assertion that time travel is theoretically impossible.....