Refactor @getodk/webform 2/2

From https://github.com/getodk/web-forms/pull/164#issuecomment-2297309308

- [ ] When using provide/inject, would be nice to establish a pattern where they use normal references so the connection between provided/injected state can be followed in editor, and types can be defined in provide. I did a quick spike on this not long ago and it seemed possible, happy to dig up the stash if there’s interest.
- [ ] Events make me nervous for reasons similar to provide/inject. They seem a bit easier to follow at component boundaries, but the lack of clear types with a single source of truth is still concerning.
- [ ] The tooling boundary between .vue and .ts modules is a continuing headache. Common case: TS/ESLint differing on whether a type is any. Case that stood out here: props interface exported from component, referenced in test. Would like to consider other approaches that minimize this. And/or set aside some time to see if any tooling updates address these shortcomings.

Start with the discussion in pull request 164 and review the three proposed areas: provide/inject state, component events, and the tooling boundary between .vue and .ts modules. Investigate whether existing patterns or tooling updates address the concerns, then define a focused scope and completion criteria before changing code.

Written by the indexing model from the issue text.