Normally the number added to the end of a file name for the purpose of editing in Photoshop or other editor is just a global counter stored in the catalog. There is no meaning or significance to the number.
You say there's "no meaning or significance" to the numbers. But you can definitely use the numbers to trace a copy's ancestry back to the source. See the tree below. For example, you can see that the parent of x-3-3-2 is x-3-3, the parent of x-3-3 is x-3, and the parent of x-3 is x. The numbers themselves tell you that.
But sadly, the numbers do NOT tell you what kind of edit was done to create the copy ("Edit a Copy Without Lightroom Adjustments" or "Edit a Copy"), which I think would be valuable information to know. In the tree below the left branches were done using "Edit a Copy" and the right branches were done using "Edit a Copy Without Lightroom Adjustments." You can see that for siblings, the only thing the numeric extensions tell you is their order of creation. It tells you nothing about the method used to create them. I'm wondering if another option in the templates would encode the missing information.
Yes, the X-n naming convention will show you the parent-child relationship and the creation order of the siblings. I would not say that it gives any significance to the number.
To encode the type of edit, you would need to manually rename the file after coming back into LR.
I agree that manual renaming is probably the solution.