The preparation of long-range entangled (LRE) states via quantum measurements is a promising strategy, yet its stability against realistic, noncommuting measurement noise remains a critical open question. Here, we systematically investigate the rich phase structure emerging from a minimal model of competing, noncommuting weak measurements: nearest-neighbor Ising ($Z_i{Z}_j$) and single-qubit transverse field ($X_i$) operators. We analyze three experimentally relevant scenarios based on which measurement outcomes are read out: complete readout, no readout, and partial readout. Using a replica mean-field theory for higher dimensions, complemented by numerical simulations in one dimension, we derive the complete finite-time and stationary phase diagrams. Our analysis reveals a striking dependence on the readout protocol. Complete readout yields a direct transition between a short-range entangled phase and a pure LRE phase. No readout (pure decoherence) precludes entanglement but exhibits a strong-to-weak spontaneous symmetry breaking (SWSSB) transition into a classically ordered mixed state. Most intriguingly, partial readout (complete readout of $Z_i{Z}_j$ with averaging over $X_i$ measurement outcomes) interpolates between these limits, featuring a mixed-state phase transition where the system can become trapped in the SWSSB phase or, for weaker noncommutativity, undergo successive symmetry breaking to reach a mixed LRE phase. A novel technical contribution is the use of a channel-fidelity-based partition function that allows us to simultaneously characterize both entanglement and SWSSB order, revealing a deep interplay between them in the replica limit. These results provide a cohesive picture for understanding measurement phase transitions, SWSSB, and mixed-state phase transitions, offering crucial insights for designing robust state preparation protocols on noisy quantum devices.

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• Open quantum systems
• Open quantum systems & decoherence
• Phase transitions
• Quantum entanglement
• Quantum measurements
• Quantum many-body systems
• Replica theory