If we're parsing at a super detailed level "Congress shall make no law abridging the freedom of speech" seems even further away from the TikTok law, if anything.
"Apple has a first amendment right to be able to list any app it wants, regardless of source" seems like the only claim you could make. The Lamont case doesn't directly apply since the government isn't an intermediary between Apple and ByteDance saying "are you SURREEEE you want to get this app from them?" And the existence of restrictions on what you can send/receive through the mail make it clear that Lamont isn't a blanket "you can't regulate messages between people" restriction.
So is "hey Apple, don't list things that meet that criteria" different than "hey UPS, don't send things that meet this other criteria"?
AFAICT the Supreme Court didn't really consider it from this angle anyway and just looked at it as a regulation on corporate control, which also seems completely legitimate. Can the US gov't say "certain things require US-person-owned/controlled companies?" They do for other things already.