What was the failure? (build logs will or have expired soon) What did you do to make it work?

Failure in core test file:

0 1) ResourcesTest::testResourceFiles
13:46:00 Less_Exception_Compiler: variable @padding-content-body-top is undefined in file /workspace/src/skins/Vector/resources/skins.vector.styles/layout-max-width.less in layout-max-width.less on line 22, column 20

The question I guess I'm asking is this: Can a skin define a skin variable that is not itself defined in core? If not, how should skins share variables via skin variables that are specific to themselves (e.g. exposed in skin styles in some way).

In short:
No and no!

These files are only meant for global skin variables shared by all skins, not skin specific variables. Skin specific values yes.
If a skin wants to define specific values, and they are not of MediaWiki's concern, it should do it in files to separate concerns.

Putting this in DST requests for now, so that we can consider documenting this (some time after the upcoming 1.0 release, as this documentation is for skin authors, not for consumers of the skin variables)

Can this be merged into T349359?