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/pencil-fill.svg

@@ -0,0 +1,3 @@
+<svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-pencil-fill" viewBox="0 0 16 16">
+  <path d="M12.854.146a.5.5 0 0 0-.707 0L10.5 1.793 14.207 5.5l1.647-1.646a.5.5 0 0 0 0-.708l-3-3zm.646 6.061L9.793 2.5 3.293 9H3.5a.5.5 0 0 1 .5.5v.5h.5a.5.5 0 0 1 .5.5v.5h.5a.5.5 0 0 1 .5.5v.5h.5a.5.5 0 0 1 .5.5v.207l6.5-6.5zm-7.468 7.468A.5.5 0 0 1 6 13.5V13h-.5a.5.5 0 0 1-.5-.5V12h-.5a.5.5 0 0 1-.5-.5V11h-.5a.5.5 0 0 1-.5-.5V10h-.5a.499.499 0 0 1-.175-.032l-.179.178a.5.5 0 0 0-.11.168l-2 5a.5.5 0 0 0 .65.65l5-2a.5.5 0 0 0 .168-.11l.178-.178z"/>
+</svg>