There are a bunch of examples of these. Excel is obviously the canonical one; almost the entire purpose of a spreadsheet is to host small fragments of an embedded value-oriented programming language which calculates the values of cells.

Other applications which lean on customisation as their entire purpose may provide entire programming languages. For example, Zapier lets you create zaps using Python or JavaScript code.

What I'd like to know is, do you know of any minimal, well-documented languages which are oriented towards producing expressions - like Excel's calculation language - which can be embedded in web application frontends or backends?

I think Lisp is still the canonical "code as data" version of this, and the question becomes just "which Lisp can I embed most conveniently?", or maybe "which Lisp has few enough features?"

Other examples in the genre are JSON Logic[1] (which is essentially a Lisp written in JSON, which sounds like a nightmare, but may be fine for machine generated logic), Lua, which is of course another full programming language, or any number of custom scripting languages used in various places.[2]

Even Dhall[3] or Nix[4] have some similarities in that they're value-oriented configuration languages, though they're quite esoteric. I don't imagine they're often used in embedded fashion.

[1]: https://jsonlogic.com/

[2]: https://github.com/dbohdan/embedded-scripting-languages

[3]: https://dhall-lang.org/

[4]: https://nixos.org/guides/nix-language.html