The easiest way is this:
- Save out your base tileset as a text resource file (save it as a .tres)
- Duplicate the file on your hard-drive; you can do this with Godot's built-in Duplicate function in the FileSystem (right-click the file) and it'll give you the option to rename the file, which I think is nice, or you can just do it in Explorer or whatever OS you're using's file explorer is.
- Open the .tres file for the duplicated file in VSCode or some text editor
- Near the top, you should see the texture which is defined for the previous tileset - replace the path for that with the path to the new texture you want to set
- Save the file and go back into Godot
This should give you a second tileset .tres file which now has the new texture with the same collision, navigation, occlusion, bitmask, priorities, icon, region, and z-index as the previous one.