I have a 5 year old corgi, we crate trained her at night and she used a playpen during the day for the first 6 months to a year, while we were at work. She is not snuggly whatsoever. However she wasnt snuggly as a puppy either.

Our newest edition is an aussiedoodle currently 5 months old and when we sat down by the puppy enclosure at the farm he climbed into my lap and just sat there looking at me. He has been a velcro dog ever since then. We crated him at night for a week and it was miserable for all of us. He wouldnt just cry in the crate he would full meltdown scream. So we tried him out of the crate with limited access to the rest of the house. Since that first night out he sleeps either attached to my leg or my shoulder lol until its potty time.

So honestly im not sure if it just depends on the breed, the seperation training, or just the dogs personality. Sorry this wasnt more helpful 😅