My observation how it is usually (but by far not always) done:

When used as an adjective, by far the most common use is US: the US team, the US spirit, the US government,...

When used as a noun, USA is the most frequent use.

So I'd expect to read:

The USA plans to invade Iran has been announced today by a White House spokesperson, but:
The US plans to invade Iran have not been sanctioned yet a White House spokesperson has announced today.

The use of US as a noun still feels awkward to me.

Wolfgang