Articulated objects are pervasive in daily environments, such as drawers and refrigerators. Towards their part-level surface reconstruction and joint parameter estimation, REArtGS introduces a category-agnostic approach using multi-view RGB images at two different states. However, we observe that REArtGS still struggles with screw-joint or multi-part objects and lacks geometric constraints for unseen states. In this paper, we propose REArtGS++, a novel method towards generalizable articulated object reconstruction with temporal geometry constraint and planar Gaussian splatting. We first model a decoupled screw motion for each joint without type prior, and jointly optimize part-aware Gaussians with joint parameters through part motion blending. To introduce time-continuous geometric constraint for articulated modeling, we encourage Gaussians to be planar and propose a temporally consistent regularization between planar normal and depth through Taylor first-order expansion. Extensive experiments on both synthetic and real-world articulated objects demonstrate our superiority in generalizable part-level surface reconstruction and joint parameter estimation, compared to existing approaches. Project Site: https://sites.google.com/view/reartgs2/home.