Default Yakuake behaviour is to open by default when the app is launched, however the option is unticked. When the option gets ticked the opposite of what it describes happens - yakuake doesn't open a new shell upon program start. (Has been like this for at least half a year)
I can confirm the same behaviour on version 24.12.3. System information: Operating System: Fedora Linux 41 KDE Plasma Version: 6.3.4 KDE Frameworks Version: 6.13.0 Qt Version: 6.8.2