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Context. Supernovae (SNe) inject large amounts of energy and chemically enriched materials into their surrounding interstellar medium and, in some instances, into molecular clouds (MCs). The interaction of a supernova remnant (SNR) with a MC plays a crucial role in the evolution of the cloud's physical and chemical properties. Despite their importance, only a handful of studies have been made addressing the molecular richness in molecular clouds impacted by SNRs. (Sub)millimter wavelength observations of MCs affected by SNRs can be used to build a census of their molecular richness, which in turn can motivate various chemical and physical models aimed at explaining the chemical evolution of the clouds. Aims. We carried out multi-molecule and multi-transition observations toward the molecular region F abutting the SNR W28, containing 1720 MHz OH masers, well-established tracers of SNR-MC interactions. We used the detected lines to constrain the physical conditions of this region. Methods. We used the APEX Telescope to observe molecular lines in the frequency range 213-374 GHz. We used non-local thermodynamic equilibrium (non-LTE) RADEX modeling to interpret the observational data. Results. We detected emission from multiple molecular species in the region, namely CH₃OH, H₂CO, SO, SiO, CN, CCH, NO, CS, HCO⁺, HCN, HNC, N₂H⁺, CO, and from the isotopologues of some of them. We report the first detection of thermally excited (nonmaser) CH₃OH emission toward a SNR. Employing non-LTE RADEX modeling of multiple H₂CO and CH₃OH lines, we constrained the kinetic temperature and spatial density in the molecular gas. The gas kinetic temperatures range from 60 to 100 K while the spatial density of the gas ranges from 9 × 10⁵ to 5 × 10⁶ cm^–3. We obtained an ortho-para ratio ∼2 for H₂CO, which indicates that formaldehyde is most likely formed on dust grain surfaces and not in the gas phase. Conclusions. Our results show that molecules as complex as H₂CO and CH₃OH can be detected in SNR-MC interactions. This could motivate chemical modeling to explore their formation pathways.