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We report $^{139}$La and $^{63}$Cu NMR investigation of the successive chargeorder, spin order, and superconducting transitions in super-oxygenatedLa$_2$CuO$_{4+y}$ single crystal with stage-4 excess oxygen order at$T_{stage}\simeq 290$ K. We show that the stage-4 order induces tilting ofCuO$_6$ octahedra below $T_{stage}$, which in turn causes $^{139}$La NMR linebroadening. The structural distortion continues to develop far below$T_{stage}$, and completes at $T_{charge}\simeq 60$ K, where charge order setsin. This sequence is reminiscent of the the charge order transition in Ndco-doped La$_{1.88}$Sr$_{0.12}$CuO$_4$ that sets in once the low temperaturetetragonal (LTT) phase is established. We also show that the paramagnetic$^{63}$Cu NMR signals are progressively wiped out below $T_{charge}$ due toenhanced low frequency spin fluctuations, but the residual $^{63}$Cu NMRsignals continue to exhibit the characteristics expected for optimally dopedsuperconducting CuO$_2$ planes. This indicates that charge order inLa$_2$CuO$_{4+y}$ does not take place uniformly in space. Low frequency Cu spinfluctuations as probed by $^{139}$La nuclear spin-lattice relaxation rate aremildly glassy, and do not exhibit critical divergence at $T_{spin}$($\simeqT_{c}$)=42 K. These findings, including the spatially inhomogeneous nature ofthe charge ordered state, are qualitatively similar to the case ofLa$_{1.885}$Sr$_{0.115}$CuO$_4$ [T. Imai et al., Phys. Rev. B 96 (2017) 224508,and A. Arsenault et al., Phys. Rev. B 97 (2018) 064511], but both charge andspin order take place more sharply in the present case.

$^{139}$La and $^{63}$Cu NMR investigation of charge order in La$_{2}$CuO$_{4+y}$ ($T_{c}=42$K)