Integrated sensing and communication (ISAC) at terahertz (THz) frequencies holds significant promise for unifying ultra-high-speed wireless connectivity with fine-grained environmental awareness. Realistic and interpretable channel modeling is essential to fully realize the potential of such systems. This work presents a comprehensive investigation of monostatic sensing channels at 300~GHz, based on an extensive measurement campaign conducted at 57 co-located transceiver (TRx) positions across three representative indoor scenarios. Multipath component (MPC) parameters, including amplitude, delay, and angle, are extracted using a high-resolution space-alternating generalized expectation-maximization (SAGE) algorithm. To cluster the extracted MPCs, an image-processing-based clustering method, i.e., connected component labeling (CCL), is applied to group MPCs based on delay-angle consistency. Based on the measurement data, an environment-aware channel modeling framework is proposed to establish mappings between physical scenario attributes (e.g., reflector geometry, surface materials, and roughness) and their corresponding channel-domain manifestations. The framework incorporates both specular and diffuse reflections and leverages several channel parameters, e.g., reflection loss, Lambertian scattering, and intra-cluster dispersion models, to characterize reflection behavior. Experimental results demonstrate that the proposed approach can reliably extract physical characteristics, e.g., structural and material information, from the observed channel characteristics, offering a promising foundation for advanced THz ISAC channel modeling.