Molecular abundances are sensitive to UV-photon flux and cosmic-ray ionization rate. In starburst environments, the effects of high-energy photons and particles are expected to be stronger. We examine these astrochemical signatures through multiple transitions of HCO$^+$ and its metastable isomer HOC$^+$ in the center of the starburst galaxy NGC 253 using data from the ALMA large program ALCHEMI. The distribution of the HOC$^+$(1-0) integrated intensity shows its association with superbubbles, cavities created either by supernovae or expanding HII regions. The observed HCO$^+$/HOC$^+$ abundance ratios are $sim 10-150$, and the fractional abundance of HOC$^+$ relative to H$_2$ is $sim 1.5times 10^{-11} - 6times 10^{-10}$, which implies that the HOC$^+$ abundance in the center of NGC 253 is significantly higher than in quiescent spiral-arm dark clouds in the Galaxy and the Galactic center clouds. Comparison with chemical models implies either an interstellar radiation field of $G_0gtrsim 10^3$ if the maximum visual extinction is $gtrsim 5$, or a cosmic-ray ionization rate of $zeta gtrsim 10^{-14}$ s$^{-1}$ (3-4 orders of magnitude higher than that within clouds in the Galactic spiral-arms) to reproduce the observed results. From the difference in formation routes of HOC$^+$, we propose that a low-excitation line of HOC$^+$ traces cosmic-ray dominated regions, while high-excitation lines trace photodissociation regions. Our results suggest that the interstellar medium in the center of NGC 253 is significantly affected by energy input from UV-photons and cosmic rays, sources of energy feedback.
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