I would put the topset/stem in a bucket or vase with water and let them develop more. I do the same thing with garlic scapes.

I would plant the onion bottom as normal, it should re-establish itself but you probably will not get another topset this season.

So how does that work, exactly? Do I break off the bulbils and separate them, then place them in a vessel where they just float in water, or should I have part of the stem under the bulbil and let that absorb water?

Perhaps just growing them in a dish with moist soil (for transplant later) would do the trick?

Piggybacking on your old thread, I transplanted my walking onions because I moved. They started growing topsets very early ans they look mature. Do i need to wait for the leaves they are attached to to turn yellow before I remove and plant? Attached a photo of one of the topsets.

If you wait, most likely all of the leaves will die - except the stalk holding the bulbils. The bulbils will be fully mature at that point. However, the bulbil in the photo looks mature enough to plant.

Yup only stalks left are the ones holding the bulbils. Ill take them off and plant them :)