How does one take complete control of the MacBook built-in webcam?
I have used Webcam Settings which you can get from the Apple App Store for US$8.  It directly adjusts the webcam (don't ask me how!) and so works with all webcam apps.  I have had no issues with Big Sur upgrade.
You will not be able to adjust everything in your list and what can be adjusted varies by webcam.  For example, it can adjust more on my Logitech webcam than the built-in webcam.
Here is the main settings panel for my built-in camera:

The Hue and White Balance settings will likely be enough to make a significant improvement.
But no app will magically make a relatively poor web cam into a great looking one. If you find the built-in FaceTime webcam is not good enough for your usage, you should invest in a better one.  I use a rather old Logitech C920 which is better than the built-in and you can easily find a webcam that is better again.