...they don't get paid to help you clean up afterwards.

Could you litigate to recover the costs and repair any damage done? Is there case law around what is a reasonable level of dishevelment?

You can file a civil suit against the police department, but results are far from certain. Unless it was a case of the cops raiding the wrong home entirely and you managed to make the news the success rate is not great.

Let's call it "extremely difficult" - https://ij.org/if-you-break-it-you-buy-it-unless-youre-the-p...

Unlikely. Similarly, if the fire department has to use an axe to chop your door open to respond to a fire call, it’s your responsibility to replace the door.