Parameter of type (arrow function) | (arrow function) is typed as never instead of union of both

Is const assertion an option for you? You can set your constant as const and you won’t have any type issues:

const cellDataFormater = {
  string: (x: string) => x,
  float: (x: number) => x,
  int: (x: number) => x,
  date: (x: string) => x,
  boolean: (x: string) => x,
} as const;

cellDataFormater['string']('toto'); // ok

Playground link