In the end, whatever happens to the nucleus is history as soon as a killer cell has detected the "infection". That's the reason for the normal side effects like pain: Cells get killed and new cells grow after the crime scene is cleared.
The real danger is in the antibodies produced, because the immune system can produce them even after the vaccine is long gone. The immune system will create maybe 200 different antibodies that bind with the spike protein (and maybe 1,000 when confronted with the real virus). The immune system has mechanisms to avoid the creation of antibodies that bind to portions of the human body, because this would provoke an allergic reaction when that part gets then attacked by immune cells. As we have seen with some allergic reactions after vaccination, sometimes the "wrong" antibodies will be produced. There is much more research needed until we have learned to avoid this.
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