I am not even sure how to ask the questions…..
I need to make this part.
How do I accurately measure the offset of the two “shafts”
You have a worn part, so you will have to extrapolate where and how the wear affects any measurements. I can't see the part to offer much help with that. Maybe there's an unworn or less worn area of it?
I'm also going to assume that you don't have a way to measure the dead nutz centerline of a tool bit on your lathe, for a single point touch off to be absolutely positively on center. That would work too, but the workaround is pretty simple....
Take the main, larger, longer shaft end, and stick it in your lathe chuck. Make that run as true as you need it to.
Take your tool post, a holder, or anything with a flat vertical surface, that you can get near to the offset, shorter part.
Manually rotate the chuck/part until the offset is directly towards you. the tool post, and the flat surface you've arranged.
Move the carriage towards the part, moving the part back and forth so the offset moves JUST above and below center.
Find the point where the part JUST touches the flat surface you've arranged at some point in that movement..
Zero your dial, DRO, or whatever. Your zero that you've just made will be one radius of the small shaft away from the centerline.
Rotate the chuck/part 180 degrees, so the offset is away from you, away from the tool post.
Move the carriage to the new offset shaft position, and find that carefuly the same way. This time it will hit the flat spot when it's off center, and on center will be loose. Gently, carefully, run right up to the point where it's touched at it's furthest extreme.
Read your dial/DRO or whatever. This reading is one shaft radius away from the centerline.
The extra radii in your measurements are both offset in the same direction, and will cancel out in the math, leaving and leave you with the exact travel reading on your dial/DRO or whatever will be the total diameter, or "swing" of the offset piece. A diameter.
Because you're looking for an offset, a radius of the "swing", dividing that number by two will give you the offset you're looking for.