This kind of thing is best done after the thesis is in the bag. A student is racing against the clock. Grad study has many kinds of hard failures. At the most extreme, your advisor could up and die. The focus has to be on finishing. That's how you get out.
Matter of fact, I did, even with help of my advisor. The journal did not take any action (it is Q1 open access journal), since they come up with all kinds of mental gymnastics why it is not copied (which boiled down it is NOT 100% the same).
That was for the first occurrence. For the 2nd one, we just did not bother because it hurts my advisor's reputation as well. It is not in the interest of journal to admit the mistake once they made it -- they will fight you about it and try to keep their reputation/image up.
