Strengthening STEM Ecosystems Act This bill authorizes the award of science, technology, engineering, and mathematics (STEM) ecosystem grants. STEM ecosystem means a network, consortium, or multi-sector partnership that is united by a collective vision of supporting participation in STEM through the creation of accessible, inclusive STEM learning experiences and opportunities with a broad range of nonfederal partners, including pre-K through grade 12 schools. The bill authorizes the National Science Foundation (NSF) to award competitive grants to eligible entities to be used for activities that draw on the expertise of those entities to improve STEM learning, the STEM network or community of practice, and workforce development, including to share best practices. The bill states that the purpose of a grant is to leverage the expertise, depth of cross-sector partnerships, and equity focus of STEM ecosystems to enhance the value of STEM-intensive organizations in improving STEM learning to address immediate and long-term STEM workforce and economic needs in states and communities. No fewer than 25% of grants awarded under this bill and 25% of the total amount awarded shall be made to eligible entities that serve jurisdictions that participate in the Established Program to Stimulate Competitive Research (EPSCoR).