> I always assumed it's 16 bit internally as well?

Correct, it's mostly 16-bit internally. Registers are 32-bit, but are split into 16-bit halves. The ALU is mostly 16-bit, but has a 32-bit shift register which is used for both shift/rotate operations and multiply/divide. There's a 32-bit adder in the "address unit" that's used for effective address calculations (including the LEA instruction), but it's much more limited than the ALU