... get her US citizenship back? Would it be relatively easy?...
Once you go through the process to formally renounce US citizenship and it’s accepted there is no do-over.
You stand in the same position as any other non-citizen in terms of gaining citizenship.
”Finally, those contemplating a renunciation of U.S. citizenship should understand that the act is irrevocable,” [exception for those under age 18}.
Renunciation of U.S. Nationality Abroad
travel.state.gov
Her issue was Japanese law incidentally. US allows for dual citizenship. As I understand it, Japan technically does not once you reach age 22. However, while I am not knowledgeable concerning Japanese law or related practices it appears that, in practice, Japan does allow it.
Given the present 'don't ask, don't tell' attitude of the Justice Ministry, it would be highly unusual if Naomi Osaka was forced to relinquish her U.S. citizenship at the age of 22.
www.japantimes.co.jp
I do not know whether Osaka went through the process of formally renouncing her US citizenship. The process of choosing Japanese citizenship per Japanese law does not suffice to acheive that result. Neither do countless articles stating she will (or has) formally renounce her US citizenship do it.