These are really great examples. I am a big fan of everything you've written about TAC, I am certainly inspired. I am incorporating this philosophy where possible on the things I work on. One potential issue I have come across is by not using classes you lose the flexibility to use different builtin elements for the main component wrapper. For example using an <article> for a card. I wonder if it makes sense to use custom attributes in more cases instead of a separate tag (like your ord button example -- as you can also apply it to a tags if someone wants a big call to action link). I've also been considering the discussion on registered custom attributes as an alternative to builtin extends with is="".
In the site-header example, would it instead make sense to do <x-siteheader role="header"> and then not need the inner <header>? What if someone wants to have a <x-card> but to show a blog excerpt where it may make sense to use <article>? I suppose you can nest it like article > x-card.
I am not sure what the right mix of custom tags, slots, attributes, classes, etc. is in some cases, when trying to build a library that may be used in ways I am not expecting. I don't want to confuse people either by having some components be tags, others as attributes or classes but I guess as long as it's clearly documented. Maybe I'm overthinking it, and if a <footer> or whatever is needed then it can just be nested. Or maybe I am still a bit too much in the mindset of how I used to build things with BEM haha