Maybe How to replace a Surface Book keyboard | Lance Bledsoe will help
If you go to Surface Recovery Image Download (microsoft.com) and enter your serial number without entering the model number, the information displayed includes the product info including model (no number). That will verify whether you have an original Surface Book, a SB2, or SB3.
Sample below.
Note that Microsoft does not sell the keyboard base separately. Some people have had luck finding them on eBay, but there is no official support for doing this.