04 — Google Sites vs GitHub Pages
A page has one host for its own document. Google Sites and GitHub Pages can be connected, but they do not become one shared copy of the page.
The difference
Google Sites hosts the Google Site. If it contains text in its own page, refreshing that site reloads Google's published copy. Text that exists only in Muse or in an unuploaded draft is not written into Google's copy.
GitHub Pages hosts the HTML file in the Meta-Sites repository. When the edited text is included in the HTML file, Git-FED uploads it, and Pages publishes it, the Pages URL serves that version again after refresh. The repository's index.html is the demonstration page for this model.
Google Sites can point to an external URL or embed website content. That connection is a route to another host; it does not make Google Sites a storage system for the external page. If an embed is blocked or constrained, use a normal link to the Pages URL instead.
Practical choice
Use the GitHub Pages URL as the source of truth for the Muse-edited HTML. Put that URL in Google Sites as a link or embed. When checking persistence, open the Pages URL itself first, confirm the text, and refresh that URL. Then check the Google Sites route separately.
For exact editor steps, see Google Sites steps. For repository publishing, see Deploy.