Does the federal government have direct authority over home schooling?
The Constitution did not grant the federal government any explicit authority over education, so home schooling, like other kinds of schooling, is mostly a matter for the states.
The federal government can and does seek to indirectly influence state and local policy by placing conditions on various forms of federal funding. The last serious consideration of any measure that would affect home schooling appears to have been in 1994. State regulations today vary widely. “Fewer than half require any kind of evaluation or testing of home-schooled children,” ProPublica reported in 2015.
At least one prominent critic, at Harvard Law, has called on the Biden administration to improve regulatory oversight, but the administration has not disclosed any such plans. Proposed legislation that would expand access to pre-K and community college makes no particular mention of home schooling.