I finally (I have been debugging this the last two weeks) found the relevant error message entries in the journal in the installer environment, which led me to [ Red Hat Bug 1914955 - Regression: Cannot install system using DVD on USB when ignoredisk is specified in kickstart: The ignoredisk entry in the kickstart file hid the USB drive from the installer.
Replacing cdrom with harddrive --partition=sdX --dir=/ in the kickstart file when booting in USB mode fixes the issue and lets the installer finish.