There are a large number of parts on my mesh that are not joined but simply two edges side by side.That worked fine when mu models static, but now that I’m animating it, the gaps become clear. I’ve tried selecting the edges that touch each other and clicking “merge by distance”, but unfortunately that seems to warp my character mesh.
You’re merging by distance incorrectly- select the whole mesh with A in Edit Mode and then Merge By Distance. Turn down the slider as needed. If that doesn’t work, you can try F3 > Fill Holes, which probably won’t help but might, and then your last option is to manually model the missing faces