chore(web): add public API for fetching keyboards without activating them

> OK, that's very side-effecty! We should have a public API for fetching the keyboard.
>
> For now I am okay with using `fetchKeyboard` here so long as we publish an API before 18.0 stable.

_Originally posted by @mcdurdin in https://github.com/keymanapp/help.keyman.com/pull/1272#discussion_r1606289845_

Our help-site keyboard documentation pages operate by fetching the keyboard, then building documentation versions of its OSK - all without formally "activating" the keyboard for use when typing. We've used undocumented, internal functionality to do so until now; it'd be wise to design a 'proper' approach and do that instead.