When she is in the pen, you need to do gradual desensitization. Just-leaving is technically flooding (ie, deal with it). This would mean she's calm in the pen, you stand up, sit down. If she is okay with that, you stand up, walk around, sit down. If she's okay with that, you stand up, walk to the doorway, go back and sit down. Stand up, go halfway out of sight, go back, sit down. I'm oversimplifying it, as true desensitization works to the dog's comfort levels and never puts the dog over threshold.
Alternatives to desensitization: occupying her attention with a food project before you depart, adding a counter conditioning component by purchasing an automated food dispenser.
In situations where you NEED to leave the room, she has now learned to climb so a pen is not an ideal option for those situations. If she needs to just 'deal with it', which is realistic for most families, I'd recommend crate over pen, and draping the crate for part of the day. If she can see you all the time then she is always 'on' and observing your movements. By removing visual for parts of the day, she can't build anticipation and react at your departure. A lot of dogs grow out of this if these anxious behaviors are not practiced (by providing a food project or removing visual) and it is a normal part of puppy behavior at this age.
It is also important (in my opinion) for puppies to learn to be alone even if there is someone home all of the time. I am not saying you need to do things the way I did. But for example, when Brae was young it was just habit that when I cooked, he was in his crate with a Kong. Or when I showered, he was in his crate with a bully stick. So instead of him thinking, "wait, why are you suddenly disappearing?" it became routine. Of course, I faded the drape over time but that then he was very accustomed to the idea that not every waking moment is about him.
Overall, some may disagree but for SOME puppies I think crating is kinder than X-pen. The pen provides more freedom. But a puppy like mine (and maybe yours, not sure) was MORE anxious when given more freedom at that age. He was certainly not settling or self entertaining. The moment he was crated, he would chew on his toys, calm down, and even sleep. So the big picture for me is, I used a lot of restriction at first but my pup seemed happier and less stress because of it. But of course, my lifestyle/household layout is different than yours. So it's up to you to find that balance.
Alternatives to desensitization: occupying her attention with a food project before you depart, adding a counter conditioning component by purchasing an automated food dispenser.
In situations where you NEED to leave the room, she has now learned to climb so a pen is not an ideal option for those situations. If she needs to just 'deal with it', which is realistic for most families, I'd recommend crate over pen, and draping the crate for part of the day. If she can see you all the time then she is always 'on' and observing your movements. By removing visual for parts of the day, she can't build anticipation and react at your departure. A lot of dogs grow out of this if these anxious behaviors are not practiced (by providing a food project or removing visual) and it is a normal part of puppy behavior at this age.
It is also important (in my opinion) for puppies to learn to be alone even if there is someone home all of the time. I am not saying you need to do things the way I did. But for example, when Brae was young it was just habit that when I cooked, he was in his crate with a Kong. Or when I showered, he was in his crate with a bully stick. So instead of him thinking, "wait, why are you suddenly disappearing?" it became routine. Of course, I faded the drape over time but that then he was very accustomed to the idea that not every waking moment is about him.
Overall, some may disagree but for SOME puppies I think crating is kinder than X-pen. The pen provides more freedom. But a puppy like mine (and maybe yours, not sure) was MORE anxious when given more freedom at that age. He was certainly not settling or self entertaining. The moment he was crated, he would chew on his toys, calm down, and even sleep. So the big picture for me is, I used a lot of restriction at first but my pup seemed happier and less stress because of it. But of course, my lifestyle/household layout is different than yours. So it's up to you to find that balance.