I'm looking for the specific statute in which Congress exercised its interstate commerce authority to actually assign this power to the FCC.
> this SCOTUS has expressed interest in reverting the interstate commerce authority to its pre-New Deal interpretations, which would disintegrate the administrative state of the last 100 years
The the post-New-Deal interpretation of the interstate commerce authority still relies on understanding that the power to regulate interstate commerce belongs to Congress, such that administrative agencies only have those powers specifically granted to them by statute.
So regardless of this, the FCC still doesn't have direct interstate commerce authority under the constitution, and can only exercise such regulatory authority as has been assigned to them by by Congress.
Whether or not those statutes will continue to be recognized by the courts as a legitimate exercise of commerce clause powers is another matter entirely.