The police officers themselves are covered by Qualified Immunity - to put it briefly, a government official acting in their official capacity in a discretionary act (as in, they have some discretion in whether/how they carry out the act) is immune from suit so long as they pay reasonable deference to relevant law. In the case of the police, so long as the search or seizure itself is reasonable (either because there is a warrant, or because they had probable cause), they can take appropriately destructive measures to carry out their duty. Even if the search or seizure is later found to have been unreasonable, an officer may still have Qualified Immunity unless their action violated "clearly established statutory or constitutional rights of which reasonable person would have known" (Harlow v. Fitzgerald). However, a search/seizure doesn't give the police license for arbitrary destruction, whatever they do has to be reasonably pursuant to the legal search/seizure. For example, if a suspect is barricaded in a house with a gun, they can knock down doors, windows and walls to apprehend them. On the other hand, that does not mean the officers can then break open safes to try and find evidence - once their probable cause for the entry is fulfilled (apprehending the suspect), they need to get a warrant to do more than a plain sight search of the house. Warrants will specify what items are being searched for, so even with a warrant the police have to take reasonable measures to carry it out - an example of an unreasonable measure would be to tear into walls in order to try and find a stolen bicycle. On the other hand, tearing into walls could be justified if their warrant included searching for drugs from a dealer, where it is not uncommon to hide them in the walls.
States and the Federal Government enjoy Sovereign Immunity from suits in most cases. There are some exceptions, but none would apply in this case so long as the general policy of the police department was not illegal or unconstitutional. However, county and city governments do not enjoy Sovereign Immunity and state governments and the Federal Government often allow suits against them for negligence from their actors, so someone injured by unreasonable police action can usually try to recover damages from the officer's department.