In this study, we delve into the intricacies of semantic communication-control codesign (CoCoCo) for wireless mixed logical dynamical (MLD) systems operating under signal temporal logic (STL) specifications. Our novel contribution, the MLD-Koopman autoencoder (AE), emerges as a method to linearize the progression of system states within a feature space. This linearization effectively mitigates the communication and computation costs associated with MLD system control. To surmount the challenges posed by multiple correlated MLD systems that possess distinct logical control rules while sharing baseline dynamics, we present the compositional logical dynamical (CLD)-Koopman AE as a remedy to the scalability limitations of the MLD-Koopman AE. This innovative approach incorporates two pivotal models—the dynamics semantic Koopman (DSK) model, capturing semantic correlations among MLD systems, and the logical semantic Koopman (LSK) model, encoding logical control rules. These models portray the linear evolution of baseline dynamics and control rules within a feature space, facilitating predictions of future states for multiple MLD systems with constrained communication. Validation comes from simulations on large-scale inverted cart-pole systems, demonstrating the prowess of the CLD-Koopman AE in achieving an average state prediction performance 82.77% higher than other predictive benchmarks, particularly evident at a signal-to-noise ratio (SNR) of 10 dB.