Author here, 'the shape of a repository' refers to the structure/organization of files/directories, file naming conventions, unicode conventions (do not allow invisible Unicode for example), making sure build artifacts aren't committed, max file size, etc. Requiring files like LICENSE, README.md, etc exist. Anything about the structure/conventions of a repo that isn't actual code (a language specific linter should be used for the actual code).
Would be interested to hear what other kinds of conventions/rules you guys find useful to enforce for a repo, and how you currently do that.