I’d go a fraction smaller with the pre drill, 5/32 is roughly the diameter of the #8 screw you’re using. You can also buy a countersink/drill combo to save you the extra step of countering after drilling.
BOSCH SP515 4 Piece Hex Shank Countersink Drill Bit Set with #6, 8, 10, and #12 https://www.amazon.com/dp/B01HH1F4PA/ref=cm_sw_r_cp_api_glt_fabc_E5KQG814YNHJYXB8JZ6W