Can I really have a proper backwash unit out there?

Yes, and it is the single question worth putting to every company you get a quote from. A backwash needs a water supply, a hot water source sized for repeated hair washing, and a waste run reaching your foul drainage at the correct falls. Where ground levels rule out gravity drainage, a pumped system solves it. An experienced garden room builder will tell you which applies at quote stage rather than discovering it once the base is down, and the room has to be properly plumbed rather than fitted with a basin and hoped for.