Community Wood Facilities Assistance Act of 2023 This bill makes changes to grant programs administered by the Forest Service to promote wood products. Specifically, the bill reauthorizes through FY2028 and modifies a program that supports capital costs for installing community wood energy systems and building innovative wood products facilities, including by increasing the maximum grant amount per facility. The bill also modifies a program that provides grants to develop and expand the market for innovative wood products. Specifically, the bill (1) modifies the grant priorities, and (2) increases the portion of a project's cost that may be covered by such a grant.