He's soooo cute!! 😁
I went through exactly the same thing when we adopted our dog. He was so destructive he chewed through a sofa, cat tree, every bed we bought him, and any cushion in sight. Barking ENDLESSLY, for everything and anything. And so much energy he was just bouncing off the walls. We had a behaviourist for a few sessions, but to be honest, none of his advice worked (maybe we just needed a better behaviourist!).
They say it takes around 3 months for a rescue dog to properly settle into their new home. I never knew this when we adopted our dog, but it really proved itself to be true. It wasn't that all problems were resolved in just a few months, but he definitely became settled and realised he was staying around this point.
Honestly, with the chewing - just go minimalist. And learn as you go along. Try out various natural chews, plus raw frozen bones if you like. We had no cushions for a whole year 😂We also blocked off bedrooms and made sure we could either always see him / have him in the same room. Then we worked on leave it, drop it, etc., and reintroduced cushions eventually. We started with cheap £1 IKEA cushions, and once we could trust him with those, we introduced more expensive ones, throws, etc. He still has a thing for cushions, but will leave or let go now. It's a work in progress and he just loves having something in his mouth.
With the barking, it just took time for us. We never thought it would be resolved, and he's a naturally vocal dog, but you get there over time. You really do have to just try things out. For instance, our dog would bark to let us know he needed to be let out, so instead, we trained him to lie down by the door. So now he does that. He'd also bark at noises, so we worked on desensitisation to noises with treats. He'd also bark for attention - and those are the barks you have to ignore. For that, we'd leave the room, wait for a millisecond of quiet, then return. Also, if you can, pop round to your neighbour, explain that to train him you need to ignore the barking, and assure them that you're working on it. We live in an apartment and basically told all of our neighbours and this stopped any complaints. We also worked on keeping ourselves calmer, not flapping around when he barked, etc.
Lastly, we stopped giving him so much stuff to do. We walk him once a day now and sometimes not at all. He just does loads better when things are calm. And when we do walk him, we pick quiet routes, quiet parks. We've noticed this really helps him overall. So now he's learnt to just chill around the house all morning, then he gets a walk some time in the afternoon, and he'll fall asleep by 7pm. We did use a pen to help get him into a sleeping routine, but of course if that doesn't work for your dog because of his history, you can just work around it. One way to do that is to have a night time routine for him. Whatever time you want him to be settling down, make time to cuddle with him, brush him, stroke him - whatever he likes. Something relaxing and soothing, and it will become a habit that signals sleep for him. :)
I hope this helps! You'll get there. Main things to remember are to keep things calm, give it time, and get inventive with solving problems. Often the solution is something totally simple, rather than going through a million steps outlined on a training video ;)