While all B vitamins play roles in energy metabolism and cell health, B12 is especially crucial for brain, nerve, and blood function
Sterile water has no preservative and should only be used if you plan to use the entire vial immediately
Further, NICE and the BNF says that if there are neurological symptoms present, then every other day injections are the recommended treatment, so all the points you make about B12 being stored and sufficient are not really relevant
In research settings, it is studied for its role in energy metabolism, nerve repair, and cognitive support
Thereby, ketamine as the model of schizophrenia in rats [193] (as acute ketamine administration was associated with schizophrenia-like or psychotomimetic symptoms with large effect sizes and an increase in positive and negative symptoms [195,196]) might escape from the extraordinary complexity of extrapolation from animal models of mental disorders in general [197,198,199]