One of the downsides this pattern has is the content shift when the notification appears:

Even with that, I think it's better than the current behavior that hides/blocks content. The Sphinx extension I built some time ago behaves in the same way: https://github.com/humitos/sphinx-version-warning

I think it's acceptable.

Take into account that the "version selector" below the title our own theme builds requires the same extra time to load.

Yeah CLS is going to be a common problem with all of this given it is injected content.

The main thing I'm still concerned with here is styling/customization, this is a more obvious alteration of user/project content than floating content. I think it would be helpful to start with something we can test without changing all projects at once, and we should aim to implement better customization before making this the default. The notification looks a bit out of place in most of the examples due to slightly different colors/borders/corners and where it lands on the page (above/below the main page title).

This is looking close and I'd agree it's getting towards a better UX than overlaying important user content.

The main thing I'm still concerned with here is styling/customization, this is a more obvious alteration of user/project content than floating content.

Would you be 👍🏼 if we inject different HTML chunk based on the documentation tool? That way, we can use the same native notification HTML structure the tool uses.

Sphinx example:

<div class="admonition note">
  <p class="admonition-title">Note</p>
  <p>Godot's documentation is available in various languages and versions. Expand the "Read the Docs" panel at the bottom of the sidebar to see the list.</p>
</div>

and it will render as:

Just an example for look and feel, the text should be the current copy we have in our own notification.

In any case, even if we have specific notification for each of the documentation tools, we still need a generic one to render when we don't know the documentation tool. I think it makes sense to focus on this generic one, first.

I think it would be helpful to start with something we can test without changing all projects at once, and we should aim to implement better customization before making this the default.

What type of customization are you thinking about here?

The notification looks a bit out of place in most of the examples due to slightly different colors/borders/corners

What changes we can do to the generic style to behave better?

and where it lands on the page (above/below the main page title).

I started writing the code to have a specific selector per documentation tool that I can continue working on to solve this issue.