Se usar IIFE você consegue ter a inferência funcionando

displayChallengePeriod.ts

import { DateTime, DurationLikeObject } from 'luxon'

const DAYS_IN_SECONDS = 86400
const HOURS_IN_SECONDS = 3600
const MINUTES_IN_SECONDS = 60

/*

const getUnit = (challengePeriod: number): keyof DurationLikeObject => {
  let unit: keyof DurationLikeObject = 'days'
  if (challengePeriod >= DAYS_IN_SECONDS) {
    unit = 'days'
  } else if (challengePeriod >= HOURS_IN_SECONDS) {
    unit = 'hours'
  } else if (challengePeriod >= MINUTES_IN_SECONDS) {
    unit = 'minutes'
  } else {
    unit = 'seconds'
  }
  return unit
}
*/


export const displayChallengePeriod = (challengePeriod: number): string => {
  if (challengePeriod <= 0) {
    return '-'
  }

  const format = (() => {
    if (challengePeriod >= DAYS_IN_SECONDS) {
      return 'days'
    } else if (challengePeriod >= HOURS_IN_SECONDS) {
      return 'hours'
    } else if (challengePeriod >= MINUTES_IN_SECONDS) {
      return 'minutes'
    }
    return 'seconds'
  })()

  const now = DateTime.now()
  const period = now.plus({ seconds: challengePeriod })

  return period.diff(now, [format]).toHuman()
}

const getUnit = (challengePeriod: number) => {
  if (challengePeriod >= DAYS_IN_SECONDS) {
    return 'days'
  } else if (challengePeriod >= HOURS_IN_SECONDS) {
    return 'hours'
  } else if (challengePeriod >= MINUTES_IN_SECONDS) {
    return 'minutes'
  }
  return 'seconds'
}


period.diff(now, [getUnit(challengePeriod)]).toHuman()