One could consider c/c line because 45bb stack villain is hardly folding better even if you barrel. OTOH it's not a horrible result if he folds KQ or something. In any case we have so much equity against almost anything that it's close to a valuebet. But if he is aggro at all v missed cbets I prefer the c/c line because more value.
Once you cbet, you are definitely not folding. Again you could just call the raise since you have no fold equity, but we have enough equity to get it in if you prefer it simple.