Where is the Basic UI sitemap HTML output being generated?

Well my guess is, you don’t.

Since BasicUI is a UI Binding I think you need to make the changes and bundle it again and install then your “custom” BasicUI Add-On/Binding.

EDIT:
Instead of assuming maybe just google or search the forum, silly me :slight_smile:

https://community.openhab.org/search?q=Customizing%20Basic%20UI