Well, we weren't "wrong" yesterday, just off the mark by about 12 hours or so. As of approximately 3:15 a.m. EDT, iTunes 7.7 is now appearing in Software Update.
This is the description from the download screen:
Use iTunes 7.7 to sync music, video, and more with iPhone 3G, and download applications from the iTunes Store exclusively designed for iPhone and iPod touch with software version 2.0 or later. Also use the new Remote application for iPhone or iPod touch to control iTunes playback from anywhere in your home - a free download from the App Store.
Thus far, I can't find any specific UI changes or option settings, so I'm assuming that the elusive "Applications" menu item will appear as soon as the App Store launches.
We'll post more details as they become available. For now, I'm going back to bed in the hopes that my BlackBerry's blinking lights won't keep me up.
Thanks to everyone who sent this in!
Update: In my partially-awake stupor I neglected to read the information about the new "Remote application" -- looks like this will be one of the first free Apple-published apps for the iPhone and iPod Touch, when the App Store launches on Friday!