Puppy is a little nightmare

Hello! I need advice on our new puppy. We have him for a few days, he's a rescue (3 months old) and he's super cute, we love him, but we're also already VERY tired. :D

When we're at home, he's a little nightmare. He barks, runs around, chews on literally everything and there's not a single second he's resting. We crate train him, so he gets at least SOME rest.

At night, he's lovely and sleeps, but if he's out of his crate, he just starts destroying everything asap and can't be redirected to toys or treats, because he doesn't care about them when he's in this state of mind. I can tell him no, distract him with something else, but he'll just ignore it completely.

My partner is at home with him, he goes to work next month and he's very tired and has severe puppy blues, because he just doesn't know what to do (and I don't know what to do, because he's just so sad and frustrated). Which doesn't help the situation, because the puppy tends to misbehave more when he's with him, because he can probably sense his insecurity.

We will contact a local trainer to get some tips, but any help is appreciated. ✨