We are getting Audio from the mic on the recorder. It sounds good, no problem with quality, just I noticed on a video where the singers were being drowned out by the music.
These two statements are at odds with each other.
If you notice that singers are being drowned out by the music, then it does NOT sound good and there IS a problem with quality.
This problem is not caused by the el cheapo wireless microphones you have. It will not be fixed with better microphones. It will not be fixed with wired microphones. It will not be fixed with a different board, or a different camera, or a different loudspeakers. It might be fixed with education.
The problem is that the audio is being recorded from a single microphone at the camera location or the recording PC, so you are getting indirect, AMBIENT sound, not direct sound from the performers. Further, if you're using the camera's onboard mic, it is likely using audio compression (they call it "automatic gain control") which makes it even worse.
To solve this problem, you need to feed the video recording directly from your board. An AUX mix bus is great for this. you can feed your recording a different mix than your house, which will let you get a better mix in your recording. The house mix is usually inappropriate for recording or live streaming.
Once you've got that done, and have an acceptable mix in your recording, then we can talk about any quality issues with your selection of microphones or your board.