Do not confuse a terminal widget which is embeddable into another application like Geany, and a terminal application like xterm, xfce4-terminal etc which are separate standalone apps.
The preferences->tools->terminal setting sets which of these external applications to execute commands in when they are set to _not_ run in the embedded terminal widget (or always on windows where that widget is not available). The setting has nothing to do with the embedded terminal widget itself.
Nothing that styles any terminal application will have any effect on a widget inside Geany, they are separate applications. The terminal widget does not [document](https://developer.gnome.org/vte/unstable/VteTerminal.html) any means of setting its colours via usual methods such as GTK style CSS AFAICT, so I believe it would not be possible to change the colours without code.
It would require somebody to write the code to read appropriate colour palette settings from the GTK style and pass them on to the terminal widget.