The key fact first: the United States does not take part in the automatic exchange of information under the OECD CRS (learn more).
Bear in mind, though, that the exchange happens at the level of the banks. Many clients open an account for their LLC with a European provider (for example Wise), and those providers are not under US jurisdiction. That puts the OECD CRS back on the table.
But the automatic exchange of information under the OECD CRS is really nothing you need to fear.
If you live, as we never tire of repeating, in a low-tax country, it is entirely normal and legal for you to have foreign income, for example from your zero-tax LLC, that you do not have to report on your tax return. So the CRS cannot hurt you either.
To put it the other way round: if you are fully tax resident in a country that does not allow the tax-optimised use of a foreign company, a zero-tax LLC is not for you.