I think it came from a bunch of material that Lucas wrote up and sent to the marketing people. IIRC it's also where the idea that Chewbacca was over a century old came from. Probably the first piece of merchandise that included that information was this movie theatre program from 1977. I know what it actually says if the Falcon is a "Corellian Pirate Starship" but I suspect that may have been misread by some as Han being a "Corellian Pirate". That or someone made a simple leap of logic: "he's a pirate with a corellian pirate ship, so he must be Corellian, right?"So what's the origin of the idea that Corellia is Han Solo's homeworld?
If I had to guess I say the first time fans were introduced to the concept would likely have been in the Marvel comics, which always played a bit fast and loose with the lore.
For the record, Lucas considered having a very young Han show up in RotS as some orphan being raised by the Wookiees, so it's possible he never considered Solo as Corellian at all.
Well we know that the Empire didn't find out about Kenobi, otherwise Vader would have gone to Tatooine personally to deal with his old master.
Sure, but the question now is "what did it take to stop that from happening and at what cost?"