Microsoft doesn't actually "repair" Type Cover keyboards — a faulty one is always swapped for a new unit, never fixed component-by-component.
Since yours is out of warranty, going through the formal Surface Service and Repair channel just adds a step — they'll tell you to purchase a replacement anyway, since self-serve accessory replacement is purchased separately regardless of warranty status.
The straightforward best move: buy a replacement Type Cover directly from the Microsoft Store rather than filing a repair/service order.