Issue with firebase typings when sharing code between frontend and backend

a.ts

// INFO: this has been simplified a maximum just to show the underlying issue

import { database as rtdbClient } from 'firebase'
import { database as rtdbServer } from 'firebase-admin'

type Database = rtdbClient.Database | rtdbServer.Database
type DataSnapshot = rtdbClient.DataSnapshot | rtdbServer.DataSnapshot

interface User {
  id: string
  name: string
}

export default async function loadUser(db: Database, id: string): Promise<User|null> {
  const snap:DataSnapshot = await db.ref(`users/public/${id}`).once('value')
  // here `db.ref(...)` will give: [ts] Cannot invoke an expression whose type lacks a call signature. Type '((path?: string) => Reference) | ((path?: string | Reference) => Reference)' has no compatible call signatures.
  return snap.exists() ? {id, ... snap.val()} : null
}

b.ts

// INFO: here is an alternative which is working...
// until you get methods calling methods... and needs huge amount of overloads
// AND for any method accepting a "shared" firebase type

import { database as rtdbClient } from 'firebase'
import { database as rtdbServer } from 'firebase-admin'

type DataSnapshot = rtdbClient.DataSnapshot | rtdbServer.DataSnapshot

interface User {
  id: string
  name: string
}

export default async function loadUser(db: rtdbClient.Database, id: string): Promise<User|null>
export default async function loadUser(db: rtdbServer.Database, id: string): Promise<User|null>
export default async function loadUser(db, id) {
  const snap:DataSnapshot = await db.ref(`users/public/${id}`).once('value')
  return snap.exists() ? {id, ... snap.val()} : null
}