Site reorg: Remove site/ subpath (#306)

Unfortunately, for proper package pathing, need to remove the `site/`
subpath. This includes:
- Moving everything back into root
- Adding a `copy-site.sh` script to copy resources into `mkdocs/site/`
before building the site with mkdocs.
- Also update examples to ensure all are loading the local sw.js / ui.js
- Consolidate examples in `docs/examples`
- Consolidate assets under src/assets/
- Move `favicons` to root
- Reformat and relint
- Tests: update playwright tests to use mkdocs output, add test for
embed in docs
- bump to 2.0.0-beta.2

mkdocs/site/docs/overrides/.icons/bootstrap/check-circle-fill.svg

@@ -0,0 +1,3 @@
+<svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-check-circle-fill" viewBox="0 0 16 16">
+  <path d="M16 8A8 8 0 1 1 0 8a8 8 0 0 1 16 0zm-3.97-3.03a.75.75 0 0 0-1.08.022L7.477 9.417 5.384 7.323a.75.75 0 0 0-1.06 1.06L6.97 11.03a.75.75 0 0 0 1.079-.02l3.992-4.99a.75.75 0 0 0-.01-1.05z"/>
+</svg>