I wasn't the only one to get stuck.
Normally in the iTunes app for iPad, there's a module on the top of "Genius" and "Featured" pages with tabs for "Featured," "Genius," and "Top Charts"—so if, for instance, you're done checking out your Genius recommendations, you can tap the "Featured" tab to leave Genius and go back to browsing.
Luckily, I found an easy fix in the Apple support forums: just tap on the Music tab in the iTunes app, make sure you're on the "Featured" music page, hit the Home button, and then restart the iPad. Voilà—all fixed. Why that particular remedy works (and there may be others fixes, too) is beyond me, but hey ... I'll take it.