No, it does not. Your link doesn’t even say as much.
It requires the President determine, “through an interagency process,” that the app is “no longer controlled by a foreign adversary” [1]. That language invokes the APA [2], explicitly rules out personal approval, and provides an objective endpoint that can be challenged in court.
[1] https://docs.house.gov/billsthisweek/20240311/HR%207521%20Up... § 2(g)(6)
[2] https://en.m.wikipedia.org/wiki/Administrative_Procedure_Act