How about you just do nothing and let her make her own decisions regarding citizenship? “should I get her citizenship?” no, it’s not something for you to give like a toy to a child. She is presumably a grown woman right?
If you are thinking about if you would like her to get herself citizenship how about asking her how she feels
can you apply for citizenship by now? If you do that you can move back to the US knowing you could go back whenever you wanted. Or to any other EU country.