Examples
Three complete sites live under examples/ in the repository. Each one is built with --strict by the same CI job as this site and published beside it, so what you see is what the configuration below produces.
They exist because the plugins involved cannot share a config with the ones this site already uses — Plugins says what breaks in each case. Read them as three things the theme does rather than as fallout from that: a site with a feed, a site whose pages are written by a script, and a site with diagrams.
A site with a feed
examples/rss/ runs mkdocs-rss-plugin, which writes feed_rss_created.xml and feed_rss_updated.xml and stops there. The theme emits the <link rel="alternate"> pair that points a browser or a reader at them, taking the filenames from the plugin's own configuration rather than hardcoding them — view the page source there and both are in the <head>.
The same site has git-authors enabled, so the footer prints who last touched the page alongside the theme's "Improve this page" link.
Pages that do not exist on disk
examples/gen-files/ builds its Generated section at build time: gen_pages.py writes the Markdown through mkdocs-gen-files, and mkdocs-literate-nav takes the navigation from a SUMMARY.md that includes it. Nothing under generated/ is in the repository.
This is the combination an API reference is usually built from, and the thing to look at is the sidebar: it nests, and its section label is a link, because section-index folded the generated index page into the section itself.
Diagrams and charts
examples/diagrams/ renders Mermaid diagrams through mkdocs-mermaid2 and Vega-Lite charts through mkdocs-charts-plugin.
Both draw in the browser, so both have to be told which color mode the page is in — otherwise a diagram is a white card in a dark article. Mermaid reads the theme's data-color-mode attribute through a JavaScript expression in that site's mkdocs.yml; the charts plugin looks for Material's attribute instead, and the page there says what that leaves you with. Neither redraws when the header toggle is used, which is why the theme fires a primer:color-mode-change event for a page that wants to handle it.
Building them yourself
Each example has its own mkdocs.yml and writes into site/examples/<name>/. Build the main site first: mkdocs build cleans site/, and would take the examples with it.
$ mkdocs build --strict
$ mkdocs build --strict -f examples/rss/mkdocs.yml
$ mkdocs build --strict -f examples/gen-files/mkdocs.yml
$ mkdocs build --strict -f examples/diagrams/mkdocs.yml