There are other metal detector projects using AVR and PIC. This one is nice and simple. I do wonder why the 7.64khz frequency was chosen instead of something in the 15k to 20k range wasn’t used.

Arduino ADC is usable around 10/12 bits. That means it can measure up to 1024/4096 diferent voltage levels. Counting frequency instead can let you choose your own diferent measurement levels ...