Discussion
1) The hydrogensulfite ion is nucleophilic. Indeed, the free electron pair of the $S$ atom makes it suitable for nucleophilic attack.
2) Alcoholate ions are strong bases. It is therefore not surprising that there is transition of the $H$ atom to $O^-$.
3) Hydrogensulfite salts of aldehydes and ketones are white solids which crystallize well. Crystallization makes the mechanism irreversible in neutral medium.
4) In strongly basic medium, the starting reagent hydrogensulfite is converted into sulfite and removed from the equilibrium: the reactions are reversed.
5) The latter is used to purify the aldehydes or ketones insoluble in water: their hydrogensulfite compound is precipitated, filtered, the filtrate recrystallized to purify it and then a strong base is added to render the purified starting reagent that must then only be isolated by decantation.
