AFAIK - there is not any "factory" supplied method to transfer global key assignments from one template to another and this includes the Normal template.
I will use the Normal template as my example for the following and know that it will also work for any custom template that is attached to the active document.
You can printout the Global Key Assignments you have made by opening any document that has the Normal template attached and selecting File > Print. From there change the "Copies and Pages" selection to "Microsoft Word".

Then change "Print What" to "Key Assignments" and click the Print button.

This will give you a list of your custom assignments. You will need to enter them again into your new global template.
I believe the only method of automating this process would be with a macro and even then I don't think it would be perfect. Here is code that will list the KeyBinding entries in the Normal template and additional code would be needed if an attempt was made
to store the bindings from one template and add them into another.
Sub KeyBindingEntries()
Dim kb As keyBinding
CustomizationContext = NormalTemplate
For Each kb In KeyBindings
Debug.Print kb.KeyString; vbTab; kb.Command
Next
End Sub
As I said, I don't believe it would be a perfect transition due to some key bindings being made to Word functions such as FileOpen or FileClose and others that might have been made to Word objects such as Styles or Symbols.
That's probably all just gibberish to most but the bottom-line is that it's complex and that's probably why there isn't any "factory" supplied method to do it.