What is the use of both I²C and UART in Bluetooth module BM78SPPS5MC2?
According to the data sheet, the UART is for host communications.

The I2C port is not for host communications and these interfaces are not alternatives to each other.

It appears, from other drawings, that the I2C port is for connecting a configuration EEPROM to the device. The data sheet doesn't go into the details of this.