  We systematically investigate the scaling behavior of the disorder operator
and the entanglement entropy (EE) of the easy-plane JQ (EPJQ) model at its
transitions between the antiferromagnetic XY ordered phase (AFXY) and the
valence bond solid (VBS) phase. We find $\mathbf{(1)}$ there exists a tiny yet
finite value of the order parameters at the AFXY-VBS phase transition points of
the EPJQ model, and the finite order parameter is strengthened as anisotropy
$\Delta$ varies from the Heisenberg limit ($\Delta=1$) to the easy-plane limit
($\Delta=0$); $\mathbf{(2)}$ Both EE and disorder operator with smooth boundary
cut exhibit anomalous scaling behavior at the transition points, resembling the
scaling inside the Goldstone model phase, and the anomalous scaling becomes
strengthened as the transition becomes more first order; $\mathbf{(3)}$ First
put forward in Ref. [arXiv:2401.12838], with the finite-size corrections in EE
for Goldstone phase is properly considered in the fitting form, the anomalous
scaling behavior of EE can be adapted with emergent SO(5) symmetry breaking at
the Heisenberg limit ($\Delta=1$). We extend this method in the EPJQ model and
observe similar yet weaker results, which may indicate emergent SO(4) symmetry
breaking in the easy-plane regime ($\Delta<1$) or emergent SO(5) symmetry
breaking in the Heisenberg limit ($\Delta=1$). These observations provide
evidence that the N\'eel-VBS transition in the JQ model setting evolves from
weak to prominent first-order transition as the system becomes anisotropic, and
the non-local probes such as EE and disorder operator, serve as the sensitive
tool to detect such salient yet fundamental features.
