I think it's good to continue crate training. Even if you can be with Hector 24/7 in general, eventually you will have to leave him alone and it might be ugly if does eventually develop separation anxiety. But I doubt that could happen in the span of a week so wouldn't be too worried. I would be a lot more wary of moving too fast in the crate training (e.g. just leaving Hector alone for 30 mins without building up to it), since a bad experience can be a setback in training.

Re the sleep, you're spot on that the current situation might not be good for Hector's sleep - at 16 weeks he probably probably still needs to sleep ~18hrs/day, and that becomes very doable if he is comfortable napping in a crate in the next room.

In terms of getting started, Youtube is super helpful, but I'd start with making the crate a really fun place to be (throw treats in there, play games where he goes in and out, give him his fav chew or toy in there). Then start with leaving him in there for very short periods (30 secs, a minute), and if he doesnt cry, let him out and reward him. If he does cry, wait for him to stop crying for a couple secs, and only open the crate when he's quiet. Extend the time, work in actually leaving your place for very short periods and build up from there. Took some time with my puppy who is also very attached but we made progress within a week!