It appears that once connecting a theme to github, the ability to one-click upgrade your theme is no longer possible. That’s understandable and all, but the Shopify documentation doesn’t seem to forewarn about it:
https://shopify.dev/docs/storefronts/themes/tools/github#limitations
Maybe it should be clear that “Uploaded themes” includes any theme connected from github, even the official ones like Dawn.
Just to prove this to myself, I tried installing a fresh, unedited Dawn theme from the shopify store and then created a github theme from those exact same files. Immediately I see the message in the upgrade tool:
Updates are not supported for uploaded themes
If you want to take advantage of theme updates, you need to install a theme from the theme store.