Does price sensitivity on a bond increase the lower the crediting rating for that specific bond?
Opposite.
All else equal, generally, bonds with long maturities and low coupons have the longest durations.
High Yield’s will have higher coupons. The interest rate move will impact them less than low rate coupons. A bond that is 3% will move more for a 1% interest rate increase than a 8% coupon bond.
Credit rating by itself doesn’t affect duration.