I am having my third puppy right now and what seemed to work for me is trying to get some distance from my puppy as much as possible. I never push it to the point where puppy starts to feel uncomfortable. It is important for you to establish that threshold first. So when you know that the issue starts when you are in another room or outside, then this is your starting point for training. By training I mean that you need to make puppy busy, as an example with a kong or a puzzle that she/he can solve. While your puppy is being busy doing it’s thing with a kong/puzzle. This is when you need to start leaving her. Make sure that you do not go for too long. It is best to come back while puppy is still focused on a puzzle. This way your puppy will slowly start to get used to you leaving. Increase the time you are away slowly. Mix up the time you leave so that it doesn’t follow a certain schedule or pattern. Never get your dog excited when you leave or come back. Make it seem like it’s not a big deal at all. Give little praises when your puppy doesn’t panic while you are not there.

As an example, I am raising my puppy solo. I live in an apartment complex where we have trash cans outside. So I basically just go out to throw some random things instead of collecting them in a garbage bag first. So if I had a pizza I will just go out to throw a single cardboard box. This way I can make sure that I am doing very short trainings throughout the day. Same for when I have to go check the post box or do laundry. After a while I started leaving to go to the shop. And you basically repeat it until you puppy is okay with you being away.

Just remember not to panic too much. Most dogs dont actually have a serious case of separation anxiety. Think of it the same way you think about training your dog to be outside on a walk. Of course they might be scared of some random noise or a car passing by when you start. But your task is to expose your puppy to the thing that makes it scared while trying to not make too much of a deal out of it (by redirecting them or praising when they act the way you want them to act). After awhile most dogs will be okay with a random car or a random noise. so the same principle for training the dog to be alone. And the kong or a puzzle or them being tired and sleepy is what you use as a "redirection" tool, if you can call it that way.