This is not how it works. Anyone in the Academy can vote on the nominees. The nominees themselves are decided by the people in their specific category.
Source: my family is in the Academy
https://variety.com/feature/who-votes-on-oscars-academy-awar...
Each person belongs to one of 17 branches. Each branch nominates for its own category — e.g., editors nominate editors, actors nominate for the four acting categories. Everyone gets to nominate best picture. For the final voting of the winner, all branches vote for everything.