The keen observer will of course know that there's no such thing as "federal immunity"

The scary thing is that there is.. you should look up "sovereign immunity". The government has complete immunity, except where and how the law permits it to be held accountable. And while we have a constitution, defending those rights through the courts requires legislation to permit it. For the most part, federal law permits lawsuits against states that violate the constitution, but have permitted far less accountability for federal actions that violate the constitution.

For example, Section 1983 of the Civil Rights Act only permits individuals to sue state and local governments for rights violations. It can't be used to sue the federal government.

There's many court cases, dating back decades, tossing out cases against the federal government for rights violations. Look how SCOTUS has limited the precedent set by Bivens over the years, basically neutering it entirely.