Calm in play pen, not outside it (and play pen activities question)

My almost 6 month old puppy (got him at 4 months) is pretty chill in his play pen but becomes a typical puppy outside of it. I WFH and during the day have him in his play pen (crate for bedtime) which is also practice for when I eventually have to go into the office. I check on him a few times and we do potty breaks, etc. Mornings and evenings are pretty much all about bonding and training.

He has a bed, food and water, toys, safe items to chew on, and usually a frozen kong. When I leave the room he ignores everything and just lies there looking sad. This is still a huge improvement from when he couldn’t stand me being out of his sight, but is this okay? If I get inside the play pen with him he’s pleased to see me at first and then will finally go for his bully stick or kong and ignore me.

I’m trying to figure out the best way to give him time/privileges outside of the playpen too but he immediately starts trying to eat things he shouldn’t or jumping on furniture. Should I just not allow him out unless I can fully supervise to help correct/redirect? He’ll play with a toy or chew on a bully stick for a minute or so then for for my shoes or rug or generally need me to pay attention to him. I tried letting him out today while I made lunch but ended up putting him back because he wouldn’t stop going for things he shouldn’t.

I’m trying to work on him choosing independent activities that are appropriate but since he ignores everything while in his play pen (unless I’m in the room, sometimes) and then doesn’t usually make good choices outside of it it’s been tough to build on that. Is there anything else I can do, or is this something to continue on and with age/maturity he’ll probably get better?

I think being out of the play pen is obviously more exciting and I want to eventually trust him to roam but we’re not there yet!