Cannot install macOS Beta version on MacBook Pro July 2019
I found this...
Catalina Link to App Store

Edit:  This link now downloads beta 5.

It may help trigger the search for updates but it didn't fix the issue for me either.

Update:  I ran the App Store link on my iMac that already has Catalina.  App Store opened System Preferences and asked if I wanted to download Catalina.  I answered yes and that downloaded the full installer.

From there I made the thumb drive from the command line and when I booted off the thumb drive it tells me that a software update is required for this Mac and clicking software update tells me that there is no update.

Running the installer from within Mojave tells me that "This version of macOS 10.15 cannot be installed on this computer."

Apparently the laptop is really unsupported at this point.