IANAL and I haven't taken a stance on this issue.
This isn't really a question of free speech. Every single one of tiktok's users in the US are still free to say whatever they want. The government is banning a business from the country, which I'm sure we've done before.
Everyone is free to exercise all of their first amendment rights, just somewhere else.
Except for tiktok itself I guess, but businesses (particularly foreign ones) don't really get first amendment rights. Their "speech" is heavily regulated for a lot of reasons, mostly very good ones.
The first amendment isn't a magical catch-all for anything we don't like about the government. It protects citizens from retaliation or punishment by the government. For instance, you can't be punished for calling your senator a dickhead, or arrested for drawing a mean cartoon of the president. Even if you want to call banning tiktok censorship, that still doesn't qualify as a 1A issue as tiktok isn't a person or a citizen of the US.