The laws that provide a right of action against the government generally don’t cover damages caused by police in the lawful exercise of their duties.

So yeah, sovereign immunity.

Even though you would think that'd be a taking for public use.

Perhaps it should be, but the courts have not agreed. See Pena v. Los Angeles for an example of an appellate case that rejected this argument. It found that a "police power" exception to the takings clause applies in such cases.