A segmented waveguide-enabled pinching-antenna system (SWAN)-based tri-hybrid beamforming architecture is proposed for uplink multi-user MIMO communications, which jointly optimizes digital, analog, and pinching beamforming. Both fully-connected (FC) and partially-connected (PC) structures between RF chains and segment feed points are considered. For the FC architecture, tri-hybrid beamforming is optimized using the weighted minimum mean-square error (WMMSE) and zero-forcing (ZF) approaches. Specifically, the digital, analog, and pinching beamforming components are optimized via a closed-form solution, Riemannian manifold optimization, and a Gauss-Seidel search, respectively. For the PC architecture, an interleaved topology tailored to the SWAN receiver is proposed, in which segments assigned to each RF chain (sub-array) are interleaved with those from other sub-arrays. Based on this structure, a WMMSE-based tri-hybrid design is developed, in which the Riemannian-manifold update used for the FC structure is replaced by element-wise phase calibration to exploit sparsity in analog beamforming. To gain insight into the performance of the proposed system, the rate-scaling laws with respect to the number of segments are derived for both the FC and PC structures. Our results demonstrate that: i)~SWAN with the proposed tri-hybrid beamforming consistently outperforms conventional hybrid beamforming and conventional pinching-antenna systems with pinching beamforming for both the FC and PC structures; and ii)~the PC structure can strike a good balance between sum rate and energy consumption when the number of segments is large; and iii) the achievable rate does not necessarily increase with the number of segments.