Congress loves giving away power to the Executive Branch so they don't have to bear responsibility for unpopular decisions. It's likely that at some point Congress gave this power to the president though not necessarily this Congress and this president. Congress is free to take the power back if it votes to do so.
Given that even the Biden campaign has prohibited their workers from installing the TikTok app, there isn't likely to be much of a partisan fight over this issue.
I mean here in France when the government or the assembly trie to pass a law that is potentially unconstitutional there is an emergency review process by the "constitutional council" that can veto all or parts of the law that infringe.
This process just happened recently because our president tried to pass a "hate law" on social media that was deemed unconstitutional because it had too many unpredictable side effects on free speech principles.
Well, showing that it's stacked by a combination of the party in power in the Senate and the one in power in the Executive; the earlier description would have been more clear with reference to which power centers were being referred to. The Republicans used being in power in the Senate to block appointments until they also held Executive power.
Given that even the Biden campaign has prohibited their workers from installing the TikTok app, there isn't likely to be much of a partisan fight over this issue.