Wow...great drawings, that really helps.
The top picture does not seem to correlate to the bottom picture: 1) the horizontal member is not painted in top picture, but is in bottom, 2) black poly sheeting in bottom picture is not in top, 3) adjacent roof rafters (that are 10” away) are not visible in bottom picture,
Nevertheless, the roof system indicates an addition was added exactly where this roof joist was added...see change in roof sheathing in bottom picture. The roof structure is not a truss, but members have been added to help support the roof.
There are several issues: 1) the roof joists are not large enough to span the 90”, 2) the lower horizontal ties (including the damaged member) help support the 2x4 roof members, 3) the damaged member does not support the ceiling finish below, as seen in the bottom picture.
Therefore, the notched member has never done much for the structural integrity of the roof. That is to say, it does not have much load on it. There is no mention of sag in your original OP. If the entire ceiling is sagging, it’s not due to this notch, it’s due to the small roof joists.
That member is essentially half the size of the adjacent members (because of the notch), but it’s carrying half the load because it’s between the adjacent members. If you must sister a joist, I’d use a 2x4 and nail (or screw) with 10d nails placed about one inch from the top edge and one inch from the bottom edge and stagger the nails so the wood does not split. Make sure there’s 5 nails each side of notch.
There is nothing in the Code that explains how to sister members or fix notched members, except that loads shall be transferred to solid members.