tl;dr: A side story film that’s incredibly similar to the main series but at somewhat higher quality, though also somewhat rushed.
Trinity Seven Eternity Library to Alchemic Girl is somewhat of a sequel film to the main series. I say that because while the original source material for the main series is a manga, the source material for this film is a spin off novel. As such, it’s not exactly filler, but it’s also not likely to have any major lasting impact on the story. It’s also very clearly designed for fans of the main series and obviously expects you to have watched that, though it does provide a quick summary at the beginning for those that may have forgotten. Still, if you didn’t like that the main series this certainly won’t change your mind, or rather you’ll probably dislike it even more.
The film essentially has two core plot aspects. The first involves Lilim, which is Lilith’s grimoire gaining a human form after sucking up Arata’s magic. As she’s born from the magic of both Arata and Lilith, she both acts and serves as a daughter like figure to both of them, which produces a good amount of fluff with both of them. She’s also just in general supposed to be really cute, which produces even more fluff with the rest of the cast. This is the focus for the first third or so of the film. After that, though it shifts to focusing on the other core plot aspect, Lilim once again becomes the focus again surrounding the climax. It’s at this point that the film feels pretty rushed. Lilim’s portion of the climax and beyond involves the viewer being invested in Lilim as well as Arata and Lilith’s bond with her in order for the emotional beats to land. While I was somewhat invested, I felt that there wasn’t enough build up in regard to investment in her for the emotional beats the film was trying to use, and thus while it did have some impact it felt like it was somewhat lacking. Thus, while there was a really solid start regarding this plot aspect, the movie felt like it pushed into the climax too quickly to really do it properly.
The second plot aspect involves a mysterious foe known as the white demon lord, Last Trinity, awakening and trying to defeat Arata to replace him. This is incredibly simple and pretty much just involves a couple small battles and a final larger one, where the cast all show their stuff and Arata even gains a new power, though I’m in doubt on whether he’ll keep it beyond this film. There is some attempt at giving the white demon lord some background that was maybe intended to make the viewer feel somewhat sympathetic towards him, but it felt very superficial and simply wasn’t fleshed out enough for it to work properly, which further leads to the film feeling kind of rushed pacing wise. Still, the action was decent enough and I’d say at about the level of the best from the main series so this felt pretty solid overall.
Beyond that, we get to see the entire cast just being themselves with their personalities shining through pretty well. How much you’ll enjoy that will largely come down to how much of a fan you are of the cast which should be clear enough from the main having watched the main series. There isn’t any major character or relationship development, but they are all still amusing with some solid comedy centered around them too.
The art and animation are pretty much the same as the main series but more polished. Overall incredibly similar, but in general the level of quality throughout is about the level the main series was at it’s best so I’d say there’s somewhat of an increase in production values but not a tremendous one. The soundtrack was as far as I can tell the same as the main series. There was a pretty solid insert song near the climax that worked well with hitting the emotional beats involving Lilim. The ED was also decent, though as is the case with most films was just credits on a black background.