It's hard to tell with the extent of information posted what exactly is going on, but it appears that the primary cause of the awkward conditions is that the slope of the addition roof is shallower than the slope of your existing roof. That in addition to the taller rafters sitting on what seems to be the same height wall is causing the roof to miss slightly at the line of the wall, and miss by a lot out at the eaves.

As I look at the elevation drawing, I would say this is a case of a design that was not fully thought through in the design phase and is likely (though I do not have all of the information to say for certain) the fault of the designer.

Solutions include redesigning and completely rebuilding the roof on the most drastic end. That is really the only way for the eaves of your old and new house to come to the same height. On a simpler fix, the portion of existing roof between the chimney and addition could be removed and rebuilt to match the new addition. This would use the chimney to hide the elevation difference, but the detailing will need to be carefully thought through so that a complicated roof geometry that is likely to leak isn't just hidden behind the chimney.

Another option may be to make the eaves of the addition deeper or shallower that the original house and just embrace that they are intentionally different.

On that note, I would be curious to see more of the built roof. If possible photos of the new roof where it meets the old roof from up on top of the roof. What is built may already be an overly complicated geometry that is likely to leak in the future.

Your builder is pretty amateur. Is he licensed and insured? Were permits pulled? What design drawings were created for the permitting process, and what do they show?

Forget matching the roof lines. That wouldn’t look good anyway. You want them deliberately different. Taller or smaller. With the same pitch. Nested. Unless you can create the addition as a cross gable.