Measurements of the branching fractions of the singly Cabibbo-suppressed decays ${D}^{0}\to \mathrm{\omega \eta }$, ${\eta }^{\left(\prime \right)}{\pi }^{0}$ and ${\eta }^{\left(\prime \right)}\eta $

By analyzing a data sample of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ collected at $\sqrt{s}=3.773\text{}\text{}\mathrm{GeV}$ with the BESIII detector operated at the BEPCII storage rings, we measure the branching fractions $B\left({D}^{0}\to \omega \eta \right)=\left(2.15±0.1{7}_{\mathrm{stat}}±\phantom{\rule{0ex}{0ex}}0.1{5}_{\mathrm{sys}}\right)×{10}^{-3}$, $B\left({D}^{0}\to \eta {\pi }^{0}\right)=\left(0.58±0.0{5}_{\mathrm{stat}}±0.0{5}_{\mathrm{sys}}\right)×{10}^{-3}$, $B\left({D}^{0}\to {\eta }^{\prime }{\pi }^{0}\right)=\left(0.93±0.1{1}_{\mathrm{stat}}±\phantom{\rule{0ex}{0ex}}0.0{9}_{\mathrm{sys}}\right)×{10}^{-3}$, $B\left({D}^{0}\to \eta \eta \right)=\left(2.20±0.0{7}_{\mathrm{stat}}±0.0{6}_{\mathrm{sys}}\right)×{10}^{-3}$ and $B\left({D}^{0}\to {\eta }^{\prime }\eta \right)=\left(0.94±0.2{5}_{\mathrm{stat}}±\phantom{\rule{0ex}{0ex}}0.1{1}_{\mathrm{sys}}\right)×{10}^{-3}$. We note that $B\left({D}^{0}\to \omega \eta \right)$ is measured for the first time and that $B\left({D}^{0}\to \eta \eta \right)$ is measured with much improved precision.