I know absolutely nothing about cameras and video production... other than they have to sync lol. I have a high res camera on my phone so I'm wondering if there's a cheap simple way to combine live audio and video ?
Maybe check your DAW? I know Reaper can do that, so yours may allow syncing of the audio with video as well. It's only about matching the timing I think - any other visual FX, transitions, cuts etc could be done with video software beforehand.
Usually a DAW doesn't allow to record video. To sync the audio with an external video and record at the same time in the DAW and your phone and everything be in sync, I think is technically possible but it is a pretty complex routing.
Your Phone connected to your Pc to the video software, your Daw stereo out set as the audio in of the video software, I never tried.
For simple projects as to make the video of a song or a live performance, the most simple way to do this is to avoid the use of another software and use the manual approach.
record the audio in your DAW while you record independently the video+audio with your phone.
This low quality audio of the phone will be used only as a guide to help you sync manually the audio recorded in the daw with the video
Mix and master the audio in your daw
import the video from your phone in your video editor of choice
Now you have a video project with the audio and the video from your phone.
Import the mastered track from your daw in the video editor software and sync it manually with the video (observing the audio waves of the 2 audio tracks will make the alignment good enough).
Mute or delete the audio track of the phone recording.
Now you can edit the video and if you need to cut again the audio you can do it also within the video editor and add fade in and fade out, volume automation, and audio processing within the video editor, or export again the audio in the daw (alone or with the video too) and then reimport back in the video editor.
Da Vinci Resolve is considered the best free video editor, you will need a little time to learn the basics but it is worthwhile the effort it has some very useful functions and the best video quality. If you look for an easier one I suggest Open Shot Video Editor