Hi and welcome.
Certainly worth screwing the neck on to see how it all fits together. The scratchplate should fit tightly around the neck and butt right up to it. The silver control plate should then locate snugly in the little semi-circular cut-out, whilst the bridge normally has a 2-3mm gap between it and the scratchplate.
If the scratchplate is a little tight around the neck so that it's hard to get it to fit, then a little sanding on the inner edges of the scratchplate should sort that out.
Note that the instruction videos are generally helpful, but with most being made a few years ago when PBG started out, they do need updating as some of the kits have changed slightly over time, which is why it's best to ask questions here and provide photographs. E.g. the Tele neck pickup is shown being screwed into the wood in the neck cavity (classic Fender-style), whereas on the kit you have, it's designed to be attached to the pickguard, which makes it easier to adjust the pickup height and also to locate the pickguard.