Is my design using 'hard' multipliers? How do I find out? How do I force it?

If you infer multipliers in your code, as you have done, Quartus needs to be able to identify all the bits around the multiplier that it needs to take and fit in to a DSP block. This includes various input & output registers.

Look at the block diagram for the DSP block. You'll see input registers that only feed the internals of the DSP block, including the multiplier.

Your 'product' signal is the product of 'a' & 'b'. However, both 'a' & 'b' feed other logic too. So Quartus can't put those registers into the DSP block - there's no path out of the DSP block for either 'a' or 'b'. Hence it can't fit your code into a DSP block and Quartus will have created it all in logic.

A sure way to force a multiplier into a DSP block is to infer a multiplier created via the IP catalogue. However, that way you'll have to work with the input/output registers in the IP and the 'extra' clock cycles required.

Cheers,

Alex