The other similr questions/answers refer to advanced set theory notation or defining exclusive functions for this. [I have answered here my own question with a middle ground solution.]
If sets were ordered, I could just do $s_1$ and get the first, also only element of the unit set $s$. But they are not ordered. Is there a shorthand for that?
Related: how to extract an element according to a single-match criterion, like pertaining to another set?
Based on parts of answers pointed by the comments, I think a good approach would be $[\{x\} \mapsto x](s)$.