Docs examples 01/14: Update live example infrastructure

Part 1 of 14 in the stack that splits up the approved draft !6295 (closed) into reviewable pieces. The content is exactly what was reviewed there; I've only sliced it.

Related to #3575.

This first MR carries the two infrastructure changes the reworked live examples rely on: the with-gl-container-queries class on the html element in nuxt.config.js, and the live_example_layout.vue adjustments. It targets main and is safe to publish on its own; the rest of the stack builds on it.