They can track it to an address. Usually the police are "no help" because 6 seconds of 180p black and white security camera footage is very little to go on.

If you can tell them that your airtag is inside 45 Elm Rd., they can knock on the door.

Assuming the police are able/willing to follow this up what happens if there's no answer at 45 Elm Rd or they deny all knowledge?

There are some stories of this going wrong the other way. Police showing up and insisting that you stole a device because the not super accurate location was reported at their address.

We even had a similar incident reported today in our nextdoor neighborhood. Someone knocked on the door at 1 AM asking for airpods since they were showing up at that location. Wifi based locationing does not work well all the time.

However, airtags work better than that since if it is within a few feet, you can get a directional view on your phone and could easily confirm if they are nearby. Also they sound loud enough that if you can get close by (inside the house), you can not miss the sound.

Could they enter under some probable cause criteria given the location of the device is reasonably known to be inside the property?

Yes but they would need to have more than just the location of some air tags, which was the case in the linked article where they were already investigating another theft.

45 Elm road? Or, with thin walls, 46 Elm road? ...throw in multiple apartments....