chore(chapter-01): organize the repo into readable workspaces

Chapter: 01 - Repository shape.

Plain-English map:
Move the project from flat `backend/` and `frontend/` folders into a
workspace layout: `apps/api`, `apps/web`, and shared `packages/*`.
This makes the codebase easier to walk because each folder has a clear job.

Why it matters:
A contributor should not need private context to know where the API, web app,
shared types, client package, or SDK live. The repo structure should teach the
project before anyone opens a README.

Principle:
Make the project legible before making it bigger. Monorepos work best when
each workspace owns one understandable responsibility.

Precedent borrowed:
The fork report showed active forks splitting concerns, adding SDK surfaces,
and creating deployment-specific structure. This commit turns that pressure
into a stable workspace map.

Upstream base: willchen96/mike@d39f580.
Original local commit: b587d63.