You can use dragon with nvda without any other software.
You did have the dictationBridge add-on which allowed you to control nvda by your voice but you would need dragon professional for that and as of this writing, the add-on is out dated. The project is seeking developers who can help. Full disclosure, I am a part of the project team.
The thing when working with speech-recognition is that many people like to hear the text that dragon has recognized. This is possible with dictationBridge but there are other solutions that can do this. Other people find hearing text distracting. That is up to you.
You will have to change 2 options for NVDA to work optimally, namely, get the dragon bar which is a kind of control center for dragon to doc to the system tray and enable MSAA for dragon menus from within the miscellaneous settings.
Why not try the windows 11 speech-recognition first and then move to dragon? When using speech-recognition, you also must get a good quality microphone and sound card.
Get a USB sound card so that it is not subjected to internal machine noise. Internal machine noise may interfere with the accuracy of speech-recognition.