If your Surface Laptop 7 is still under warranty, I would suggest contacting Microsoft directly and opening a warranty service request rather than relying only on the authorized service provider.
Since the service provider has already diagnosed the problem as a motherboard failure and has requested the replacement motherboard from Microsoft, make sure you mention this clearly in the Microsoft support case. Also mention that your warranty is expiring soon and that the service provider has told you Microsoft has not supplied the required part.
Go to your Microsoft account and check Devices → Surface Laptop 7 → Get service/Start order. If you can create the service order, do it before the warranty expires. Keep the service provider's job sheet/diagnosis and any communication showing that the motherboard was requested.
I would also keep the service provider's job number and the date you originally submitted the laptop. Those details may be important if Microsoft needs to verify that the problem was reported while the device was still under warranty.