1. Enable joystick controller option. Ship pitch and roll can now be controlled from the stick
2. You have a problem in that you are not able to map the joystick buttons to keys directly as the controller menu is apparently setup for a console gamepad instead.
3. The solution to the above is google for a program called Joy2Key. This program allows you to map keyboard commands to the joystick directly saving a lot of time and hassle.
I have a HOTAS and tempted to use the stick for ship control - it has more than enough buttons for the majority of boff powers and ship command functions.
If anything this can be an entertaining alternative control method - even if there is not enough buttons on the stick, you can either map shift or alt commands via joy2key... or imagine it as a sort of manual override.
Ships with high turnrate are going to be very sensitive so map the deadzone accordingly using external joystick configuration or preferably the manufacturer's driver software, if any.
The controller interface in STO, I repeat, is by default setup for 'digital' control such as like from a Xbox controller.