The Board of Mediation was formed May 20,1926
You can see the Board of Mediation was abolished June 21, 1934, you can see it was changed to the National Mediation Board.
§154. National Mediation Board First. Board of Mediation abolished; National Mediation Board established; composition; term of office; qualifications; salaries; removal The Board of Mediation is abolished, effective thirty days from June 21, 1934, and the members, secretary, officers, assistants, employees, and agents thereof, in office upon June 21, 1934, shall continue to function and receive their salaries for a period of thirty days from such date in the same manner as though this chapter had not been passed. There is established, as an independent agency in the executive branch of the Government, a board to be known as the "National Mediation Board", to be composed of three members appointed by the President, by and with the advice and consent of the Senate, not more than two of whom shall be of the same political party. Each member of the Mediation Board in office on January 1, 1965, shall be deemed to have been appointed for a term of office which shall expire on July 1 of the year his term would have otherwise expired. The terms of office of all successors shall expire three years after the expiration of the terms for which their predecessors were appointed;
I have no idea what mediation board you think Biden created, if he did Congress had no part in it and anything they come up with cannot be backed by law or statute.
It doesn't exist, If Biden actually said this he lied again.