refactor(structure): convert part-of files into libraries with explicit imports (staged by layer)

## Problem
(verified) `lib/main.dart:63-148` lists 79 parts; all cross-file references are invisible (no imports), `main.g.dart` serializes types from across the app into one generated part (main.dart:148), and private members are effectively global.

## Proposed fix
Mechanical, staged conversion: `data/` first, then `view_models/`, then `ui/` — each file gets its own imports (and `.g.dart` part where needed); a shared barrel file can smooth the transition. Do this *before* moving files into feature folders so each file moves once. Sequence after #597's call-site renames to avoid merge pain, or coordinate branch ordering with it.

## Acceptance criteria
- [ ] Zero `part of carp_study_app` directives
- [ ] `dart run build_runner build` still generates correctly (per-file `.g.dart`)
- [ ] App builds and runs in local + CAWS modes

**Effort:** L · **Priority:** P1 · **Change risk:** Medium (large mechanical diff; compiler verifies, but rebase-heavy — slice per layer)