Add mixin method-collision detection script

[zntznt]

Problem

The App class is split across 7 mixin files (app-props.js, app-demos.js, etc.). Each copies methods onto App.prototype via Object.defineProperty. If two mixins define the same method name, the later one silently overwrites the earlier — no linting, no warning, no test.

Plan

Add a small Node script scripts/check-mixins.js that:

1. Parses each mixin file for class AppXxx { ... } and extracts method names
2. Reports any method name that appears in more than one mixin
3. Exit 1 if overlaps found

Run as a pre-test step.

Effort

~30 minutes. New file only. ~30 lines of Node.js.

[zntznt]

Implementation Order

This is Phase 3 · Step 3.2 — implement after #47.

Priority: LOW-MOD
Phase: 3 (Structural / Developer-Facing)
Order: 8 of 10
Depends on: Nothing
Effort: ~30 minutes