What's the purpose of using PNP transistors on I2S bus?
These are level shifters from 1.8 V to 3.3 V (actually, only close to 3.3 V, but "close" counts in horseshoes, hand grenades, and digital inputs).

They are based on a diode offset level shifter. See Microchip's 3V Tips 'n Tricks for a longer explanation, but in short, by inserting a diode between the 1.8 V output and the 3.3 V input, and by adding a pull-up resistor to ensure that there is always a current flowing through the diode, the output's low/high voltage levels are shifted up by about 0.7 V:


So a low signal of 0 V is shifted to about 0.7 V, which is (just barely) below the guaranteed low switching threshold of 1 V of the PCM5102's input, while a high signal of 1.8 V is shifted to about 2.5 V, which is (just barely) above the guaranteed high switching threshold of 2.3 V.

There are two problems with this:


When the CSR64215 is driving a low signal, its output must sink all the current. It has an output impedance of up to 100 mV/mA, so with 2.6 mA, the combined voltage drop over the output and the diode can result in an output signal larger than 1 V.
When the CSR64215 is driving a high signal, its output must still sink all the current, which flows into the 1.8 V power supply. If there is not another part of the circuit that uses up that current, the power supply can float up to a higher voltage.


To reduce the current that the low-voltage device must be able to sink, the diode has been replaced with the emitter/base junction of a PNP transistor:


This behaves the same as the diode (i.e., you get the same voltage drop), but now most of the current flows into ground. (In this common-collector configuration, the base voltage is never lower than the collector voltage, so the transistor cannot saturate, and the base current is determined by hfe, which is about 100.
The base resistors (R18/R19/R20) are not actually needed.)



Compared to an integrated level shifter like the SN74AVC4T245, this transistor circuit  has a much smaller noise margin, uses more power, and generates switching noise on the power supply. But it's a little bit cheaper, which is the primary design goal of these Chinese boards of unknown provenance.



Actually, the CSR64215 can run its digital outputs at 3.3 V, but I guess that the bluetooth module used on your board is not available in that configuration.