Ah, okay: Literally EVERY other pack of Effekseer animations I've ever used for MZ tells me to drag the individual animation files into the Effects folder, which is what I did at first... I still don't understand why your animations don't work using that method because all the others do, but after I simply copied the entire folder instead of just the files, it worked instantly. Thanks!
Effekseer needs proper filepathing to work, and that means the animation files need to have the same relative position to the texture files.
Since a few updates ago, RPG Maker MZ has allowed subfolders inside any asset folders on RPG Maker. As subfolders make projects tidier I decided to implement them -- by dragging the whole folder instead of just dumping its contents on the Effects folder, you can have your animations separated in tidy self-contained packages. Makes updating, erasing or adding new content much easier! But yeah, it's a bit different from other packs. I'm glad it worked out! Thank you!