Gas transport simulation in bentonite for radioactive waste disposal poses challenges for numerical models due to its complex microstructure. Understanding the processes involved is a prerequisite for assessing gas flow's impact on repository layouts. The DECOVALEX23 (D-2023) Task B (Large Scale Gas Injection Test: LASGIT) project aims to advance numerical techniques for predicting gas flow in repository systems through gas injection tests on compacted bentonite at the British Geological Survey (BGS). This study develops a comprehensive coupled hydro-gas-mechanical 3D numerical model to simulate the test, considering heterogeneous initial permeability and embedded fractures. Addressing bentonite swelling, three gap closure scenarios for the canister-bentonite blocks gap interface were considered. The model reproduces observed test behaviors, capturing preferential gas flow paths. Sensitivity analysis explores variations in volume factor sensitivity, calibration, hydraulic conductivity of interfaces, heterogeneity, permeability, and model parameters, contributing to a deeper understanding of the phenomenon's complexity. The proposed hydraulic modeling, enriched by considerations of gap closure states, predicts measured evolution of gas injection trends. suggesting reliability and potential applicability for similar conditions and facilitating a comprehensive analysis of its impact on gas testing processes. Additionally, the embedded fracture models underscore the critical role of fracture behavior and dilatancy in determining the system's hydro-mechanical response, with significant sensitivity to these factors influencing stress and pore pressure evolution. Hydro-mechanical models demonstrate that modeling approaches involving embedded fractures and dilatancy significantly influence gas pathways and entry gas pressure. System volume plays pivotal role in the analysis, while sensitivity analysis of contact transmissivity reveals potential influences on preferential gas pathway formation. Hydraulic and hydro-mechanical modeling methods show promise for further numerical investigations, indicating potential for yielding meaningful insights in future studies.