Next generation cellular deployments are expected to exploit the 6-24 GHz frequency range 3 (FR3) and extremely large-scale multiple-input multiple-output (XL-MIMO) to enable ultra-high data rates and reliability. However, the significantly enlarged antenna apertures and higher carrier frequencies render the far-field and spatial stationarity assumptions in the existing 3rd generation partnership project (3GPP) channel models invalid, giving rise to new features such as near-field propagation and spatial non-stationarity (SNS). Despite extensive prior research, incorporating these new features within the standardized channel modeling framework remains an open issue. To address this, this paper presents a channel modeling framework for XL-MIMO systems that incorporates both near-field and SNS features, adopted by 3GPP. For the near-field propagation feature, the framework models the distances from the base station (BS) and user equipment to the spherical-wave sources associated with clusters. These distances are used to characterize element-wise variations of path parameters, such as nonlinear changes in phase and angle. To capture the effect of SNS at the BS side, a stochastic-based approach is proposed to model SNS caused by incomplete scattering, by establishing power attenuation factors from visibility probability and visibility region to characterize antenna element-wise path power variation. In addition, a physical blocker-based approach is introduced to model SNS effects caused by partial blockage. Finally, a simulation framework for near-field and SNS is developed within the structure of the existing 3GPP channel model. Performance evaluations demonstrate that the near-field model captures higher channel capacity potential compared to the far-field model. Coupling loss results indicate that SNS leads to more pronounced propagation fading relative to the spatial stationary model.