When this tag is copied and pasted, the resulting tagname: test1
...then pasted again: test2
Given the following tag: test123
When this tag is copied and pasted, the resulting tagname: test124
...then pasted again: test125
Why are the zeros dropped in the paste, but the non-zero values are not dropped in the paste?
Also, when either starting tag (test001 or test123) is used in UDT edit; the copy / paste does not create an additional tag ... doesn't event try to create an incorrect tag and doesn't throw an error. Why?
As far as your first question, I assume that it's removing alpha characters, casting to an integer value, increments it, and then concatenates it back together.
001 = 1, but 100 != 1; therefore, 124 is incremented to 125 because the 1 and 2 are significant digits. Leading zeros do not mean anything in decimal formatting.
The core answer to your question "why does it work this way" is that it's the way we programmed it, unsatisfying as that answer is. @dkhayes117 is essentially correct about how it works.
The copy/create additional logic has been essentially unchanged for 10+ years. It's possible it's bugged a thousand people in that time, or only just you. If you want it to work differently (your request is reasonable), the best way to get that to actually happen is to open a feature request; that's one of our most useful signals to help determine if in fact there are a thousand of you out there frustrated by this, or if it's just you.