Are SMs authorized to advertise in uniform?

If the SM is actively and knowingly involved in the video, then the regulations and policy are quite clear (at least according to Army regulations ... assume it's the same with the other Services).

AR 670-1 (Wear and Appearance of Army Uniforms and Insignia), Paragraph 3-7:
k. Wearing Army uniforms is prohibited in the following situations:
(1) In connection with the furtherance of any political or commercial interests, or when engaged in off duty civilian employment.

There are many different policies that DoD has (uniform regs, social media policy, etc.) which all have a common theme buried in them somewhere: You can't imply that DoD supports an outside activity by wearing a uniform, using your official position, and so on except in some defined limited circumstances.

While the first part of that (political) is the one that usually gets the most attention (you can't go to a political rally in uniform, etc.) going against the second half will get you in as much trouble as the first.

It SOUNDS like this is what you are describing ... a Soldier making a TikTok video promoting a private business while he's wearing his uniform. If, as pointed out by SSG Carlos Madden, it's a TikTok video promoting the business that show Soldiers in uniform at it, then that's a different thing.

While I agree it is confusing, and I agree with the other responders; there have been a recent barrage of insurance legal firms stoking the Marine base contamination, throughout the various deliveries they depict people in uniform.

For me, as I understand the literature you cannot be involved in political events and the like and you cannot do anything that would be disparaging to the military or the country.

As the Major says, if it doesn’t feel right it probably is not

I think it would be hard to enforce if there is something and it would have to be really specific. For example what if someone posts them eating Micky D's at lunch with their friends? Someone could say "the perception is that the military is endorsing that company."