We study the trade-off between secret message (SM) and secret key (SK) rates simultaneously achievable over a state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. Thismodel subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. An inner bound on the semantic-security (SS) SM-SK capacity region is derived based on a novel superposition coding scheme. Our inner bound improves upon the previously best known SM-SK trade-off result by Prabhakaran et al., and to the best of our knowledge, upon all other existing lower bounds for either SM or SK for this setup. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message-key distributions. The achievability proof uses the strong soft-covering lemma for superposition codes.