Background: The presence of alkali species in ground-based spectra of comets is complex. The observed abundance ratios deviate from solar composition, suggesting alkali ejection from phenoxides reacting with carbon dioxide at the nucleus surface. Methods: Here we search for the emissions of the alkali in spectra of the coma and of the trail of Comet C/2023 A3 (Tsuchinshan-ATLAS) exploiting the double-fiber entrance of the very high resolution PEPSI spectrograph at the 8.4m Large Binocular Telescope. Results: Spectra sampling the nucleus yield $Na/K$ ratios about four times higher than the solar value, and even higher ratios sampling the trail. This fact excludes photodesorption as the main sodium source, leaving phenoxilation at the surface of the main nucleus and the trail mininuclei as the primary sodium source. Conclusions: The C/2023 A3 nucleus temperature and the faint KI line exclude potassium phenoxylation. For the first time, KI is detected in the trail of a Oort cloud comet, being potassium photodesorbed from the trail mininuclei. Sodium phenoxylation is at least six times more efficient than sodium photodesorption if the $Na/K$ ratio in the C/2023 A3 nuclei is chondritic. Trails composed of sub-km-sized mininuclei may be common features of Oort cloud comets.