No problem. Playing a bass isn’t much fun when it doesn’t work like it’s supposed to.
On the outside chance that the pup checks out ok with the multi meter and the pot checks out ok with the multi meter and the neck pup is sending a clear signal to the output jack and the tone knob is functioning you will have narrowed the issue down to wiring. The wiring diagram you posted is correct. So follow each wire in the bass and make sure it matches the diagram and you should be good.
If still no luck it could possibly be one if a couple of oddball situations - maybe a broken wire hidden inside the insulation. I had that happen with an instrument wire not too long ago. It took a bit of head scratching to figure out because sometimes it read perfect continuity and other times not, depending on which direction the wire was bent. About the only other oddball situation would be from over heating the mesh ground wire when soldering, to the point it degraded the insulation between it and the hot wire thus shorting out the signal from the pup, but maybe only when the wire is bent or wiggled in a certain direction. The odds of either of those things happening in your case is slim to none.