Reorganize JS folder structure to avoid huge folders

Currently, we have several folders with a lot of files in core. `components` is especially egregious. We might want to split these up a bit, although how exactly we want to do this is up for discussion.

Start by inspecting the JavaScript folders under core, especially components, and review the existing discussion before proposing a structure. The issue leaves the exact organization open; done would require an agreed folder layout and corresponding moves without breaking references.

Written by the indexing model from the issue text.