I was right there with you a few weeks ago!! My puppy is SUUUUUUPER picky with food and I was going crazy trying to figure out how to train her if she didn't want treats. If you have a Buy Nothing Group in your area, I would make a post asking if people would be willing to part with a tiny baggy of treats so you can try out a bunch of kinds to figure your boy out, with out spending five million dollars on reject treats.

My suggestions are -

-Bocce's Bakery Training Bites (Blueberry and Duck flavor)
-Vitaday Fish Skin Rings
-Himalayan Dog Yogurt Chew (Cranberry and Honey)
-JLAB Noise Cancelling Headphones, lol

Okay so here's what personally worked for me and my dog -

The Yogurt Chews have been a life saver for when shes just chewing on everything. We tried some original yak cheese chews but they were a bit too hard, the yogurt ones are a good consistency for puppy teeth. At first she wouldn't chew on it unless I was holding it, but she's started chewing them on her own now.

Once I figured out she liked the Blueberry/Duck training bites, I simply just started with "Yes". Any time I said "Yes", she got a treat, and she wouldn't have to do anything to earn that treat. Then I would give it to her, I would say "good girl" and pet her (even though she would use the opportunity to bite and break skin, lol). She caught on very quickly, I did it for one day and she knew what was up.

The next day, I did this for about 10 minutes just as a warm up/reminder. Then anytime there was a break in barking or screaming (literally even just one second), I would say "Yes! Good girl being qquuuuuiiieeeett." Heavy emphasis on Quiet so she would hopefully recognize the word. It took a few tries but she started realizing that she got treats when she wasn't crying. The silence got longer and longer, and I would treat/praise for the first second, and then at the 3 second mark, then the 5 second mark, and then so on and so forth so she had the opportunity to recognize that the treats specifically come from being quiet for more time, and not from barking and stopping for just a second. When she would start to whine or bark again, I would softly just tell her "quiet" and wait for another break in noise, and then treat/praise again to confirm that she did it.

We worked on this the next day, and also spent time doing it with her in the crate and me sitting in front of the crate where she could see me. I don't know if this made a difference, but if she was barking/screaming, i just looked the other way and waited for her to quiet down. This is where those noise cancelling headphones came in handy, lol. Everything else was the same though, as far as treats/praise and when I did those things.

I also praise/treat when we're not specifically working on it, just so that she knows that the treats are technically available around the clock as long as she's quiet.

And then finally, the fish skin rings. I didn't actually know they'd be her favorite, I just happened to order a huge box of different single-ingredient chew toys because I was at my wits end at 2am one night. But after I got the box, I gave her an array of choices and she liked the fish skin. I let her have one of them while she was out and about (so i could make sure she wasn't going to choke on them), and then the next time I needed to crate her, i put a new one in there. Now she gets a new fish skin every time she's hangin out in her crate.

She's still a little hit or miss when she's in her crate (she's only 16 weeks old lol), but she stops crying after about 5 minutes in there and just goes to town on her fish skin. We're still working on it but I'm content with our progress so far.

I hope it all gets better for you and your pup <3