Advice needed about leaving puppy

Hello everyone, first post on this /r.

My wife and I got a standard Schnauzer on December 30th. Dante the Bark Knight is currently 3 months old puppy.

We have a crate, that he enjoys since day one, sitting, chilling, sleeping overnight in it, taking his naps. Whenever we leave tho, if he is not asleep beforehand, he would throw a tantrum. We've left him 3 times with a camera to record so we can revisit those times.

1st time – he was asleep in the crate, we left for 25-30 minutes, no sound, no cry, when we got back, he heard us, and he woke up

2nd time – he was settled in the crate quietly, we left, came back 30 minutes later, watched the video for 18 minutes, he would cry and bark with some short pauses, on the 19th minute mark, he would lie down whining, and then we would be back

3rd time – we gave him a frozen Kong and left, first 10 minutes he would chew on the Kong unbothered, then for 2 minutes he would do singular barks + whines with big pauses. From minute 12 to minute 16, he would pace in the crate, whine, and bark with almost no pauses. Minute 16-17 he would check the Kong again, he would start barking again, escalating but with pauses, he would then proceed to lie down for a minute and whine, and then suddenly jump and escalate again. Once he hears the front door, he would sit and be quiet.

Our issue is i work from home, wife goes to work, his crate is in the living room and we live in an apartment block. We need to be able to do groceries and go out every now and then for tasks without him making the neighbours mad. I literally cant go to the toilet without him as he starts scratching the door and crying, not so much that he is attached to me but that he is alone, if wife is in the room, he is chill. We can't leave him out of crate fully yet as he never naps and he eats everything (piranha stage).

Thing 2:

At night, when he is crated ready for bed, (potty, water ), if we leave right away he starts throwing tantrums that are keeping the neighbours on edge, so we started staying a little longer til he falls asleep, then leave

Any advice is welcome.

P.S commands he knows
Home,

Bed,

Break (to release him from command)

Sit,

Here,

Stay (work in progress)

Edit: Some info and commas