For HQQ 1bit, a group size of 8 needs 2 fp16 numbers (you mentioned 8bit for shift). So you need 8 * 1bit + 16bit + 8bit for each group ie 32bits for each group size of 8. Or 4bits per param.
I'm assuming the scale and zero_point are both moved to 8bit maybe so 8*1bit + 8bit + 8bit = 24bit / 8 = 3bits per param?
"This version offloads the meta-data to the CPU, so only the binary weights and the low-rank adapters are stored in the GPU memory.", so the 8+8 scale / zero_point moves to the CPU. So GPU memory 1bit, but CPU meta data is the rest - very smart!