Did Nagarjuna want to become a Buddha? Did Nagarjuna aspire to Buddhahood in a way that he wouldn't be a 'ariyasavaka' type of disciple who attains awakening to the truth during a Buddha's sasana?
In brief, the Mahayana has a specific Bodhisattva vow not to wait:

To abandon: Believing and saying that followers of the Mahayana should
remain in cyclic existence and not try to attain liberation from
afflictions.

Those authoritative texts in the Mahayana which seem to contradict this are only for purposes of training the mind. This is not a subject of controversy in the Mahayana as every tradition acknowledges the above.
Again, with emphasis so this is absolutely clear: All Bodhisattva's in the Mahayana path make a vow to reach full and complete enlightenment as fast as they possibly can. That means if a Buddha was alive right now on this earth and they could possibly reach full and complete enlightenment in the next millisecond, they would do so without question forthwith.
See here for the long answer.