basically:
- record both with the camera and into the DAW
- import the video (and its audio) into a video editor project
- edit the recorded (non-camera) audio in the DAW until you are happy
- export the DAW audio as an mp3/wav/etc
- add the audio file to the video editing project and put it on the timeline just under the camera audio
now, if this is a pro level video package, select “sync audio” or whatever the equivalent is. If the software won’t do it automatically, then use the old school method - manually drag the audio on the timeline and visually line up the new audio file with the one the camera recorded, looking for sharp transient peaks like snare drum hits. This is much easier than it sounds, but feels tricky the first time.
When happy, mute or delete the camera audio track.
You can use the same method to add the backing track.