Growing tall like a tree is a sign of not enough light. Did the stem break or just bend?

You could cut it, allow it to harden off, then replant in a pot with a hole using cactus and succulent mix combined 50/50 with perlite. Don't water for a week at least.

Might be an echeveria but I'm poor at identification.

Could possibly be an Echeveria purpusorum. The leaves have the right shape and the speckled pattern, but purpusorum is much darker in color

It reminds me of purpusorum as Emily said. Color could be too light because of not enough light. Cooler temps also intensify the color. Or maybe it is one of the hybrids.

IIRC, E. purpusorum is not easy to grow from leaves, and is mostly propagated from seeds. If your plant is E. purpusorum and you are lucky and get a leaf to root, pls. let us know and post a photo.

I would behead it if trunk got too long or broken, just as socks suggested.

Leaves to root usually do not need to callus for days, and most of the time should be put on or into a dry mix. Too much moisture could cause rotting. But, I never tried to root leaves of E. purpusorum, so maybe I a wrong. Good luck!

The plant is in an eastern window, gets a lot of morning sun. I've seen succulent leaves that fell into my pebble tray under the pots take root. So we'll see with this guy. Maybe the light is not intense enough to bring out the reddish color of the leaves.

Yes, it probably isn't intense enough. Windows cut down the light quite a bit, and even more if there is any protection on them. And morning sunlight is more 'gentle'. I keep my haworthias and sansevierias in east-exposure windows, since they do well in less sunlight. Even now, while all plants are outdoors, those plants get sunlight until about 11:00 am only - there is never enough space with sunnier exposure for all high light plants :) Did you have leaves of this exact plant to root? Maybe I'll take some off my plant and see if I have any luck. Many echeverias (and other succulents) will root from leaves readily, but few are more finicky.