Knaster forcing preserves Suslin trees

If $T$ is a normal splitting Suslin tree and $P$ is Knaster, then $P\times T$ is CCC, so $P$ forces that the ground tree is still CCC Countable levels and splitting persist. A new cofinal branch would give an uncountable antichain by splitting, so none is added. This permits adding many Cohen reals while retaining a Suslin tree, and distinguishes Knaster preservation from an unjustified preservation claim for every CCC forcing.