For some reason avr-gcc toolchain builds still doesn't have the Atmega328PB, but it's easy to add. I followed the guide below with some minor deviations such as for the io.h entry I did this instead:
#elif defined (__AVR_ATmega328PB__)
The version of avrdude I have already includes support for the 328PB, so I didn't need to make any changes there. For Linux Mint, the avr directory is located under /lusr/lib. Another thing to note is that after the changes are made, the 328PB is still not shown with avr-gcc --target-help but it does work.