Does a dentist insert and apply any object into the dry socket during a wisdom tooth extraction.

Typically, yes. It will be packed with some gauze after the extraction.

They don't put anything IN the socket after an extraction. They may place sutures and/or have you bite down on gauze.
Now, if it is a DRY socket a day or 2 after the extraction then yes, they will put a thin medicated gauze strip in the socket.

Oteddy, flossie's answer is best. I do recall now, that the only reason that they packed my sockets with gauze was because I did have dry socket. I had forgotten that after over 20 years.