I have now finished moving! My anime collection has, of course, moved with me, and it looks much the same as before, with a couple of additions, and subtractions
As it turns out, despite the move, I actually still have no more room for shelving, so this is all I've got for the foreseeable future. With this in mind, in an attempt to claw back some space, I've put all my DVDs in storage, apart from the ones I haven't seen yet, and once I've seen them, they'll be joining the others. This will hopefully buy me some time so I can figure out a better long term solution.
One upside with this new house is that I have a second room to put my TV in! I have a couch and a proper TV stand now and everything, which I'm just thrilled about. I was miles away from my TV before, so to be right in front of it is genuinely great and makes it feel twice as large! I was thinking about getting a newer, bigger TV, but now I'm close to it, it seems rather unnecessary.