Q.Aloe repotting
One of my aloes has become wobbly in the pot due to the fact tha I have tended to remove ‘leaves’ from bottom up. I have just removed some babies and am not sure whether I can just sink the parent deeper in new compost.
Planting the Aloe in deeper will likely cause rot in the stems, I would not advise.
It is difficult to propagate an Aloe do to the high moisture content in the leaves. Removing the pups as you did is the way to propagate the plant.
You may want to keep it happy and harvest the remaining leaves as needed.
Aloe Vera are quite inexpensive and it may be time to treat yourself with a new plant.