13 weeks old Border Collie puppy advice needed

Hello everyone and sorry for the long post,

Hope this post reaches the right people that have been in a similar situation and can give some advice from experience.

We have a bundle of energy and joy, a 13 weeks old Border Collie puppy. Her name is Rey(yes, as in the Star Wars character) and she has been with us for 5 weeks now :). She is a great puppy! She bites quite a lot, she pulls on the leash when walked, she rough plays with my brother’s cat, and misbehaves at times, but she is a puppy so we know that with training and time we will correct those behaviours together. However, we want to ask for advice is regarding 2 things:

  1. Mental enrichment / physical exercise:

So, we know Border Collies are an extremely intelligent breed and also extremely active dogs. Therefore, we try to fulfil her needs as much as we can. We train throughout the day (so far she knows “sit”, “down”, “paw”, a bit if “heel”, she has decent recall unless she gets distracted by something way more interesting than us/food, “place”, “stay”, “crate”, “take it”/“leave it”, and we are working on “off” for when she jumps on the furniture or on us). We also play with her, either tug or throwing a ball/stick around and get her to bring it back. She has loads of chew toys, but she is barely interested in them (unless she is in the crate/pen and she has nothing else better to do). We feed her in lick mats, snuffle mats, puzzle balls or Kong, and the food that doesn’t get used during meal times gets used in training (She is food obsessed). We take her on 2 walks a day (one early in the morning and one in the evening). However, we feel like she still doesn’t get enough of both as she would never nap on her own(she used to nap all day in the first week with us but not anymore), so we have to enforce naps in the crate. Any recommendations on what we could be doing with her to tire her out so she would sleep on her own?

  1. Crying in the pen/crate:

So, our girl sleeps all night in the crate and lately she does not cry/whine when put in the crate at night time. During the day she is crated for enforced naps or when we have to work/run errands. Sometimes she whines when we put her in the crate to nap, but not always. She does however cry when she wakes up (not sure if it is because she wants to let us know that she is awake or she just seeks attention). But the main issue is that she cannot be left alone in a room (outside of the crate). If we leave even for a second and the door closes behind us, she starts crying and barking for a few minutes until she settles down.

I understand if she cries in the crate because she is enclosed, but when we try to train her to be alone in a room she is usually either in the pen/roams free. Based on behaviourists I watch online, this is a sign of isolation distress (as they are extremely social creatures, they hate being left alone).

But my question is, anyone has any recommendations on how to tackle this?
We are trying to build distance/duration but we can’t even close the door without her starting to cry straight away.

Overall, many thanks for any advice or information anyone could provide. ☺️ Here is a pic of our girl🖤