First, selecting the "Stream Paused" option in the inspector will stop the music because... well, the stream is paused. The values in the inspector are the initial values for the node and will not change.
Anyway, I'll just go through this step by step.
Click on "Project", "Project Settings", and then "Input Map". Add a new action by typing in a name (like "pause") and clicking the "Add" button.
Click the "+" next to the action and then select the option that you want to correspond to the action. Since you want the player to hit a key on their keyboard, select "Key" and hit the key on the keyboard that you choose. Click "OK".
In the scene docker, click on your AudioStreamPlayer. Press the scroll with the green plus sign to add a script to the player.
Replace the auto-created script with this:
stream_paused = !stream_paused
That's all the steps! You do not have to follow these steps exactly, and I encourage you to look up more information about the nodes you're using so that you can understand this better. If you need more help, I can send you an example project.