Categorically eligible means considered income eligible for free meals or free milk, as applicable, based on documentation that a child is a member of a Family, as defined in this section, and one or more children in that family are receiving assistance under SNAP, FDPIR or the TANF program, as defined in this section. A Foster child,Homeless child, a Migrant child, a Head Start child and a Runaway child, as defined in this section, are also categorically eligible. Categorical eligibility and automatic eligibility may be used synonymously.
https://www.law.cornell.edu/cfr/text/7/245.2 says:
This follows from https://www.law.cornell.edu/uscode/text/42/1758#b_5 which provides discretionary authority for states to entitle these children.
The USC and CFR also should replace the current reference in https://github.com/PolicyEngine/policyengine-us/blob/master/policyengine_us/parameters/gov/usda/school_meals/categorical_eligibility.yaml