How to correctly send the data I received via I2C over UART?
You are sending a zero, the problem is that you want to see a printable representation of 0 which is character code 0x30, not raw value 0x00.

You'll either need a terminal program which can display raw vales as a hexdump, or to write code on the Atmega side which expands each byte into a two character hex representation or an up to three character decimal one.