I would repot it deeper but idk

The part of the stem under the soil is all the way to the bottom of the pot. Bigger pot is not possible.

In your picture, above the dry leaf, looks like a root nub. Can you look around and see if there are more? This happened to my large one and I chopped it off below the root nubs but left enough to stick in the soil, and propped it up with rocks.

Here it is now, just checked it and it is sturdy.

What does the rest of your plant look like?

I also wonder about whole plant - most leaves look like they are not in great shape? Pls. post photo showing whole plant. I also think it should be beheaded, question is how far to cut. Maybe few leaves should be taken off too.

Aloe will root after beheading, but shouldn't be kept wet until roots grow.

Sharp knife to cut the stem, let it dry out a bit before potting it up. The lowest leaf or two should be removed because if they are buried they will just rot.

7" of stem above the pot is not wobbly, but actually very solid.