Added case 2 and updated the reproduction.
Case 2 is moving an element to other element withou waiting. For now it will do nothing as disconnectedCallback and connectedCallback happen in one micro task. I suppose at this case we should unmount the element and re-mount it to update parent?

I think this usage is not quite right. Vue adds many private properties to custom elements. You can't continue to use the element that has been removed from the DOM tree. because the private properties still on the element will cause some edge cases. You should add a new custom element instead.

But manual DOM manipulation should be allowed as it's a standard web feature.
We're simply using native methods remove and append, not using any private properties.
True we normally don't do these operations, I found these issues during writing Cypress test cases, during which I found element was removed and appended back on every test snapshot.
If it's totally under Vue I agree with you, but I believe customElement feature can be used in vanilla HTML and JS, we shouldn't take what users will do for granted. I can use Vue to write custom elements and ship them to everywhere(which is I'm doing), so please consider to fix this, Thanks!