You mention discoloration but it isn't showing in the photo.

I suspect that the root cause is that the house and the addition are settling at different rates because the crack is 'deep'. IOW's not a case of the drywall corner tape lifting due to moisture or being mud starved under the tape.

Of course you need to investigate any potential leak issue--like roof to sidewall flashing, etc. That will mean a trip to the attic for tell-tale signs of leaks.

If this is caused by settling differential, perhaps crown molding may be the easiest way to disguise it. Filling and repair will likely be only a temporary fix at best.

Also, you need to be sure that the foundation, footings, etc. for the house and the addition are in good repair and meet specs for the load & soil conditions. (As well as grading & runoff management--gutters, downspouts, etc.)

I have added another photo where you can see some discoloration on the ceiling in the corner. I went into crawl space attic above to see if I could find any signs of water damage and I could not though I couldnt get as close to that space as I would have liked. None of the sheet rock appears moist to the touch.