Indeed. It looks to me like the export here is probably ThreeJS STLExporter? It is known for creating non-watertight models, unfortunately.
PrusaSlicer seems to do an adequate job tidying these up automatically.
I think it's not particularly uncommon for STLs exported from common CAD packagers to have some of these issues, though this is a lot.
Super-nice otherwise though -- a neat design. And in general I think client-side tools like this have a lot of potential. Three.js opens up potential for doing task-focussed things without using OpenSCAD on a server or a full emscripten build of OCC (like Cascade Studio does)
The only thing that looks a bit bad is that the models produced need to be fixed before being able to be sliced.