Ownership of unlisted foreign corporation

The fact that you're naturalized and were born in the UK mean nothing.

What matters are:

1. whether Germany is under some sanction by the US (it's not),
2. whether or not Germany allows foreigners to own stakes in Germany companies (you can),
3. if there's a limit on how much of a company that a foreigner can own,
4. taxes (both US and German), and
5. how to register your ownership with the German authorities.

Great details on you're naturalization as a US citizen and being born in the UK, they are highly relevant.

This is because many foreign companies do not want the additional burden of dealing with a "US Person" because it may create a compliance burden with them for reporting US taxes. What many US Persons do is create a non-US business entity and invest through that.

They operate in a US-ecosystem and simultaneously operate in a non-US-ecosystem.

But this doesn't matter yet until you figure out how to buy the shares of the German company. If you have a seller, then your citizenship does not prevent you from buying. There are then things you can do to make yours and the company's life easier, such as investing with a Cayman Islands business, for example. Then your tax burden is on you exclusively.