According to this Wall Street Journal report, Huawei is suing the
What does this really mean?
Are they suing the entire U.S. government, a branch of the U.S.
government, the people of the U.S., or something else?
This means that he is either (1) suing the United States government as an entity, or (2) a federal government official, in either (a) an official capacity action seeking injunctive or habeas corpus relief, or (b) in a personal capacity in a Bivens action (suing the official for violating his constitutional rights).
It is not possible to sue "the people of the U.S."
It is also not possible to sue a branch of the U.S. government unless it is an independent agency with a federal corporate charter that gives it the right to sue and be sued in its own name (e.g. the U.S. Post Office or AMTRAK or the FDIC). You cannot, for example, properly sue "the Commerce Department" or the "IRS", although a generous judge might treat such a suit as a suit against the United States of America.
The jurisdictional statute (5 U.S.C. § 702) cited in the Complaint states (emphasis added):
A person suffering legal wrong because of agency action, or adversely
affected or aggrieved by agency action within the meaning of a
relevant statute, is entitled to judicial review thereof. **An action in
a court of the United States seeking relief other than money damages
and stating a claim that an agency or an officer or employee thereof
acted or failed to act in an official capacity or under color of legal
authority shall not be dismissed nor relief therein be denied on the
ground that it is against the United States or that the United States
is an indispensable party. The United States may be named as a
defendant in any such action, and a judgment or decree may be entered
against the United States: Provided, That any mandatory or injunctive
decree shall specify the Federal officer or officers (by name or by
title), and their successors in office, personally responsible for
compliance. Nothing herein (1) affects other limitations on judicial
review or the power or duty of the court to dismiss any action or deny
relief on any other appropriate legal or equitable ground; or (2)
confers authority to grant relief if any other statute that grants
consent to suit expressly or impliedly forbids the relief which is
The pleading linked by @Putvi, in that answer, indicates that the suit is against the United States of American and against several U.S. government officials in their official capacity seeking declaratory relief and injunctive relief in a U.S. District Court for the Eastern District of Texas (i.e. (1) and (2)(a) above, but not (2)(b)).
And in which type of court will this lawsuit be heard?
A suit against the U.S. as an entity seeking money damages is brought in the U.S. Court of Claims. But, usually, such actions are either for contract disputes, or plain vanilla negligence torts where there is a waiver of sovereign immunity (e.g. a routine car accident against a Department of Commerce official driving carelessly from one work site to the next in an official vehicle an causing an accident).
In this case, however, it is a suit brought in a U.S. District Court which has jurisdiction over all forms of suits against federal government officials and separately incorporated entities whether seeking money damages or injunctive relief, and suits against the United States as an entity that do not seek money damages. (FWIW, If I recall correctly, U.S. District Courts also have jurisdiction over inverse condemnation actions and eminent domain actions even though they are claims for money damages against the United States.)
The nominal defendant in a habeas corpus action is the prison warden or comparable jail official (often a sheriff).
Even if there were a mix of federal and non-federal claims, the U.S. District Court would have jurisdiction over the non-federal claims via both supplementary jurisdiction and diversity jurisdiction.