Why didn’t the firing of the ring at the end of Halo 3 wipe out all life?
Halos only have a 25,000 Light Year range and it was outside the galaxy. It also misfired because it wasn’t operational yet, and the premature firing caused it to explode instead of actually emitting the pulse that would have obliterated all life in range.
To put some actual numbers to it, Installation 00 was stated by Guilty Spark to be “two to the eighteenth light years from galactic center”, so 262,144 ly. Which is over ten times the effective range of an individual pulse (25,000 ly). On top of that, Earth is about 27,000 ly from galactic center. So that puts the Ark at 263,530-ish ly from Earth by way of the Pythagorean Theorem. You could imagine similar numbers for other inhabited worlds.
And even if that’s not completely accurate due to curved spacetime and all that, you get the idea. Even if 04b was able to fire a full-on pulse, the galaxy was well out of harms way by virtue of distance. Remember: space is big.