My question is quite simple though I cannot find anything that points to it in the documentation.
I am generating documentation for a project with the default generator in Antora but I cannot figure out how to customize the top navigation bar, items on the right side, which have some defaults.
Since the site is generated, where should I change, or how, those items? I do not want to list such items there.
Yep, you need to build your own UI. The docs for that are available here: https://docs.antora.org/antora-ui-default/
Like Matt said, you'll need to check your
header-content.hbs
handlebars.