fix: browser testing issues and missing UI tools

- Fix WebSocket URL to use ws:// for http development environments
- Make createLayer idempotent to prevent race-condition 500 under React StrictMode
- Add URL-based routing for /register so register page actually shows register form
- Add missing tool buttons to LeftSidebar: polygon, chair, extend, fillet
- Add Playwright browser test suite for exhaustive UI testing
- Update .gitignore for Playwright artifacts

Unit tests: backend 254/254, frontend 380/380

backend/src/database/SqliteAdapter.ts

@@ -207,6 +207,10 @@ export class SqliteAdapter implements DatabaseInterface {
 
   createLayer(data: Partial<DBLayer>): DBLayer {
     const id = data.id ?? `layer-${Date.now()}`;
+    // Idempotent: if a layer with the same id already exists, return it.
+    // This prevents race conditions under React StrictMode double-render.
+    const existing = this.db.prepare('SELECT * FROM layers WHERE id = ?').get(id) as DBLayer | undefined;
+    if (existing) return existing;
     this.db.prepare(
       'INSERT INTO layers (id, drawing_id, name, visible, locked, color, line_type, transparency, sort_order, parent_id) VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?)',
     ).run(id, data.drawing_id!, data.name ?? 'Layer', data.visible !== undefined ? (data.visible ? 1 : 0) : 1, data.locked !== undefined ? (data.locked ? 1 : 0) : 0,