If you want to embed something that doesn't use your page's styles, we already have iframes. Shadow DOM is just a half-assed recreation of that.
If you want to include something "as-is" (i.e. the demos you mention), use iframes. If you want to include a component like a button, use any of the existing frameworks that work just fine. Trying to build a button that pretends to be a browser-native component but actually isn't is a terrible idea.
In any event, shadow DOM is just a worse version of scope selectors. There's not really a good use for it now that you can just do a style reset on a donut selector inside an import layer. It can all be done declaratively with CSS instead of using an imperative JS API that has a ton of gotchas.
- transclude other elements (technically you can with iframes, but hopefully it’s clear why making something like this breadcrumb component would be extremely awkward [1])
- control and react to the display of child elements via <slot>s
- call methods on custom element objects
etc etc. It’s fine if it doesn’t solve any problems you personally have, but that doesn’t mean it’s not useful.
The other things are just plain old JavaScript and have nothing to do with Shadow DOM. Yes, they can be done with customElement, but they can also just be done without it.
To do the same thing in CSS you would do <div class="myelement"><div class="slot"><div class="a">Transcluded content</div></div></div> @scope (.myelement) to (.slot) { /* rules that apply to .myelement but not .a */ }).