Veterans Economic Opportunity and Transition Administration Act This bill establishes the Veterans Economic Opportunity and Transition Administration to administer economic opportunity assistance programs for veterans and their dependents and survivors. Specifically, the Veterans Economic Opportunity and Transition Administration must administer the following Department of Veterans Affairs (VA) programs: vocational rehabilitation and employment programs, educational assistance programs, veterans' housing loan and related programs, and the Transition Assistance Program. Prior to the transfer of administrative responsibilities, the bill requires the VA to certify that (1) the transition of the provision of services will not negatively affect the provision of such services to veterans, and (2) such services are ready to be transferred. The bill also establishes a cap on the number of full-time equivalent employees authorized for the Veterans Benefits Administration and the Veterans Economic Opportunity and Transition Administration for FY2024 and FY2025. Finally, the bill extends certain loan fee rates through November 30, 2031, under the VA's home loan program.