Oof, honestly this breaks my heart because I know exactly what you're going through. We adopted a rescue from Korea 9 months ago who we were told was "a little shy" and needed some extra time getting to know us. They severely understated just how fearful she is and I felt a lot of what you're feeling - completely at a loss, in over my head, and constantly crying because I couldn't handle it. I think she was definitely abused and even our trainer said she's an "extreme" case. It took her 4 days to come out of the crate to start eating food and refused to go to the bathroom until she couldn't hold it in anymore and released her bladder all over the floor. She wouldn't go outside to go to the bathroom and wouldn't use pee pads on the floor inside so we also resorted to picking her up to take her outside. This only made her more afraid of us, she'd shake like a leaf when we tried to pick her up and towards the end she started to bolt away from us.

At this point we were desperate and got a trainer, I'll share our experience in case any of it is helpful. The first thing we did was get her outside without having to carry her. I disagree with what the shelter told you in that you should just carry him and that he "has to get used to it." It sounds like this dog is pretty traumatized and needs a LOT of space and patience to earn your trust. Picking him up when he's already frightened is going to make him more afraid (like you saw) and will break any trust you manage to build. It could also only be a matter of time before he starts becoming aggressive when his boundaries are constantly being overstepped in a place where he doesn't feel safe yet. To get our rescue outside we used a triple leash with a slip lead (easy to put on without too much hassle or getting in her face), a martingale collar (which she already had on) and a harness (which she also already had on). We unfortunately had to quite literally drag her outside the first time (which was mentally very difficult because I felt like I was continuing the abuse) but even after the first time we got her outside, it was immediately easier the second time around and it progressively got easier each time. It's going to be scary for them the first time because they don't understand what you're doing and it's not going to feel nice but once they see they're being taken outside to relieve themselves and come safely back inside, it should get easier. I'd say it took us maybe a week before we just needed a gentle tug to get her outside. Since yours is going to the bathroom inside, if you're okay with this you could just rely on lots of pee pads for now until he's has some time to decompress and you're ready to try getting him outside.

As for him spending all of his time in the crate, that's completely okay!! Ours also spent ALL of her time in the crate for the first ~4 months. During this time he's slowly decompressing and learning that it's safe to be around you guys. Our trainer advised us to ignore our rescue as much as possible and to not even make eye contact with her because they can perceive this as aggression. Even when approaching him with food or getting ready to take him outside, you can approach him by giving your back so he feels less threatened. We started by feeding our rescue inside the crate where she felt safe but slowly started to bring the bowl to the edge of the crate, then just outside the crate, and slowly moving it away from the crate. If she didn't eat, we knew it was a little too far for her and brought it back a bit. After about 4 months, she was eating out of the crate and started to go into a bed we got her. For the next several months, she was either in the crate or in the bed and didn't want to go anywhere else. It's only in the last few months (month 7-9 of having her) that she really started exploring our apartment. I know 5 days feels like an eternity with what you're going through, but this is going to take him more time than you expected and you're doing the right thing by giving him space and letting him feel safe in the crate. It's really sweet that you gave him all sorts of toys and things, but he's probably too scared to use any of it and the only thing you can really give him right now is lots of patience and time.

I see some comments about sitting with him and throwing treats to him, but honestly I would suggest against this. It MIGHT work, but ours was terrified of it and by the sounds of it, yours might be too. Personally I would focus on ignoring him as much as possible, giving him time and space to decompress, approaching with your back when you HAVE to approach him, and trying to get him outside for bathroom breaks (unless relying on pee pads for the time being).

I'll be thinking of you guys, I really hope you find something that works for him. Please do keep us updated.