This work addresses semi-passive Reconfigurable Intelligent Surface (RIS) architectures enhanced with radio-frequency (RF) chains for receiving pilot signals via tunable absorption phase profiles. A novel channel estimation protocol is presented, according to which the RIS receives non-orthogonal training pilot sequences from two multi-antenna terminals via tunable absorption phase profiles, and then estimates the respective channels via its baseband processing unit. The proposed approach exploits beamspace sparsity and low-rank properties of extremely large MIMO channels and is efficiently solved via the Alternating Direction Method of Multipliers (ADMM). Numerical results demonstrate advantages over existing benchmarks and showcase the effectiveness of using RIS-side channel estimates to dynamically optimize phase-quantized reflection coefficients.