Some people over think things.
Fill reservoir, start engine, top up reservoir, turn steering lock to lock until steering feels good topping up if needed, and job done. Any remaining air in the fluid will work it’s way out once it’s been sat for a while. Steering boxes aren’t much different from racks in terms of bleeding, as they’re still essentially a double acting ram.
Yes, in an ideal world a hydraulic pump should never be allowed to pump air/gas, but it takes a lot of cavitation before you do enough damage to cause noticeable damage. I’ve seen power steering pumps run with no fluid for several days, yet they still work fine once the system has been fixed and fluid refilled.