Found it on the curb, and I liked the design. Looks like solid wood, but the joints are all coming apart and look tricky to reinforce. Would you bother?
If you have the time there’s no harm, but you’re probably going to want to disassemble the steps to repair it halfway well.
Depending on the weight of the person/people who will be be using it, you might want to rethink the design or make the steps out of something thicker/beefier. Since the two treads are essentially cantilevers, the riser and torque is all that’s prevent the far end of either step from collapsing. I don’t think a butt joint is good enough here, even if it has a backer (as the pictures show). A finger joint between the treads and the riser, with many smaller fingers, is probably your best bet. You’ll probably want a table saw and a jig/slead to cut them, unless you’re familiar with a good alternative and/or have the skill and time to do it with hand tools.
Depends how short you are…
As someone who isn’t a woodworker, but enjoys having things that make me happy- if you like the design and it makes you happy, go for it. You have nothing to lose but time, and if you learn something in the process (i.e. those tricky looking joints you mentioned) then you are ahead no matter what.
I’d do it, though I might cut new side stretchers and do a full mortise and tenon through the legs; maybe also add a cross stretcher between.
But I agree, looks pretty neat