Eitrigg has the followup to the Warchief’s Command quest, not Saurfang.
If Eitrigg doesn’t have “Machines of War” then you’ve got something causing phasing issues. Keep in mind that just being eligible for certain quests can cause the phase to change, so just abandoning (or never picking up) these quests won’t fix your phasing.
If the character hasn’t done the BfA intro, that’s the first thing to do as that will mess with the Orgrimmar phasing. (You might also need to pick up the Heart of Azeroth. The Earthen Guardian NPC near the Zuldazar Harbor flightpath will have “A Dying World”.)
If you have done BfA stuff, then the later parts of the War Campaign can cause phasing issues as well. You’ll have to finish those up if that’s the case.