  We examine the dynamics of a $(1+1)$-dimensional measurement-only circuit
defined by the stabilizers of the [[5,1,3]] quantum error correcting code
interrupted by single-qubit Pauli measurements. The code corrects arbitrary
single-qubit errors and it stabilizes an area law entangled state with a $D_2 =
\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry protected topological (SPT) order,
as well as a symmetry breaking (SB) order from a two-fold bulk degeneracy. The
Pauli measurements break the topological order and induce a phase transition
into a trivial area law phase. Allowing more than one type of Pauli measurement
increases the measurement-induced frustration, and the SPT and SB order can be
broken either simultaneously or separately at nonzero measurement rate. This
yields a rich phase diagram and unanticipated critical behavior at the phase
transitions. Although the correlation length exponent $\nu=\tfrac43$ and the
dynamical critical exponent $z=1$ are consistent with bond percolation, the
prefactor of the logarithmic entanglement growth may take non-integer multiples
of the percolation value. Remarkably, we identify a robust transient scaling
regime for the purification dynamics of $L$ qubits. It reveals a modified
dynamical critical exponent $z^*\neq z$, which is observable up to times $t\sim
L^{z^*}$ and is reminiscent of the relaxation of critical systems into a
prethermal state.
