  We extensively study long-time dynamics and fate of topologically-ordered
state in toric code model evolving through projective measurement-only circuit.
The circuit is composed of several measurement operators corresponding to each
term of toric code Hamiltonian with magnetic-field perturbations, which is a
gauge-fixed version of a (2+1)-dimensional gauge-Higgs model. We employ a
cylinder geometry with distinct upper and lower boundaries to classify
stationary states after long-time measurement dynamics. The appearing
stationary states depend on measurement probabilities for each measurement
operator. The Higgs, confined and deconfined phases emerge in the time
evolution by the circuit. We find that both Higgs and confined phases are
separated from the deconfined phase by topological entanglement entropy. We
numerically clarify that both Higgs and confined phases are characterized by a
long-range order on the boundaries accompanying edge modes, and they shift with
each other by a crossover reflecting properties in the bulk phase diagram.
