Strengthening Organic Agricultural Research (SOAR) Act of 2023 This bill requires the Department of Agriculture (USDA) to expand organic research, including through grant opportunities and the collection of data. Specifically, the bill reauthorizes and increases funding for the Organic Agriculture Research and Extension Initiative, a grant program which funds projects to enhance the ability of producers and processors who have already adopted organic standards to grow and market organic high quality agricultural products. USDA may also provide competitive grants for research, education, and extension activities regarding the transition from nonorganic production systems into organic production. The grants may be offered for the purposes of overcoming social, economic, and management barriers to organic transition; documenting and understanding the effects of organic practices on ecosystem services (e.g., soil health and fertility); and developing improved technologies, methods, models, and metrics for transitioning to organic management. USDA may prioritize grants for proposals that actively involve certain historically Black colleges and universities, tribal colleges or universities, and Hispanic-serving agricultural colleges and universities. The bill also provides additional funding for the Organic Production and Market Data Initiatives to collect data and report on the production and marketing of organic agricultural products. Further, USDA's Economic Research Service must conduct an economic impact analysis of organic agriculture and submit a report to Congress. The report must include an analysis of farming and ranching operations and the economic impacts, both direct and indirect, of organic agriculture on rural and urban communities.