Government ownership rarely shows up by name on a supplier's shareholder list. It usually sits a few layers up.
Under the prohibited foreign entity rules, the government of a covered nation counts as a specified foreign entity, and the law says that includes any level of government below the national level, along with its agencies and instrumentalities. So does an entity those bodies control, which for a company generally means owning more than 50% by vote or value. A provincial or city investment group can matter as much as a national one.
In company filings and registries, phrases like "state-owned", "state-owned assets supervision", "government guidance fund", "industrial investment group" or "development investment company" often point to a government owner a layer or two up. None of them settles anything by itself, but each is a reason to keep tracing.
Some links can't be confirmed from public records: nominee holdings, private fund investors, or terms in contracts that were never filed. Those become questions for the supplier, and the answers belong in your evidence file.
See also: how to read a company filing for ownership and control
General information, not legal or tax advice. Whether a particular entity is a prohibited foreign entity is a question for your counsel.