[Free the USA]

If you are willing to do a little research you will find that the reason the Fourteenth Amendment mentions "State" is because, up until that time the Constitution was considered to only be limit on the power and authority of the Federal Government. With the Fourteenth Amendment many of the Constitutions protections where extended to preclude State Government actions.
From the Third pargraph of the below linked reference.

The reference in the 5th Amendment applies only to the federal government and its courts and agencies. The reference in the 14th Amendment extends protection of due process to all state governments, agencies, and courts.

Constitutional Topic: Due Process
USConstitution.net

[outlawcam]

the reason the Fourteenth Amendment mentions "State" is because, up until that time the Constitution was considered to only be limit on the power and authority of the Federal Government

It is true that there was a debate about who was affected by the Bill of Rights, but it is not true that it "was considered to only be [a] limit on the power and authority of the Federal Government." If I may rearrange the words so that it is more accurate, "Many people considered it to only be a limit on the power and authority of the Federal Government, so Congress acted to close any argument on the matter by the state and federal courts, as well as the state legislatures, not necessarily because they agreed with the assessment."