This paper proposes a novel adaptive dual-path framework for covert semantic communication (SemCom), which integrates covert information transmission with task-oriented semantic coding. Unlike conventional covert communication methods that embed hidden messages through power-domain signal superposition, our framework embeds covert data within task-specific features via semantic-level intrinsic encoding. This new architecture introduces dual encoding paths with adaptive block selection: an Explicit path for public task execution and a Stego path that jointly encodes both public and covert information through contrastive representation alignment. A Gumbel-Softmax enabled adaptive path selection mechanism dynamically activates network blocks based on task require- ments. We formulate a multi-objective optimization framework that simultaneously ensures accurate semantic understanding and reliable covert transmission. We rigorously evaluate our framework's security against a powerful, independently trained attacker. Experimental results on the Cityscapes dataset demon- strate a state-of-the-art level of covertness: our method suppresses the attacker's detection accuracy to a near-random guessing level of 56.12%. This robust security is achieved while simultaneously maintaining superior performance on the primary semantic tasks compared to the baselines.