Add unit tests for LoginButton component with comprehensive coverage

.github/copilot-instructions.md

@@ -8,6 +8,7 @@
 - **Database**: Use TinyDB with `from_dict()`/`to_dict()` for serialization. All logic should operate on model instances, not raw dicts.
 - **Events**: Real-time updates via Server-Sent Events (SSE). Every mutation (add/edit/delete/trigger) must call `send_event_for_current_user` (see `backend/events/`).
 - **Changes**: Do not use comments to replace code. All changes must be reflected in both backend and frontend files as needed.
+- **Specs**: If specs have a checklist, all items must be completed and marked done.
 
 ## 🧩 Key Patterns & Conventions
 
@@ -15,7 +16,11 @@
 - **Scoped Styles**: All `.vue` files must use `<style scoped>`. Reference global variables for theme consistency.
 - **API Error Handling**: Backend returns JSON with `error` and `code` (see `backend/api/error_codes.py`). Frontend extracts `{ msg, code }` using `parseErrorResponse(res)` from `api.ts`.
 - **JWT Auth**: Tokens are stored in HttpOnly, Secure, SameSite=Strict cookies.
-- **Code Style**: Follow PEP 8 for Python, and standard TypeScript conventions. Use type annotations everywhere in Python. Place python changes after imports. Place all imports at the top of the file.
+- **Code Style**:
+  1. Follow PEP 8 for Python, and standard TypeScript conventions.
+  2. Use type annotations everywhere in Python.
+  3. Place python changes after imports. Place all imports at the top of the file.
+  4. Vue files should specifically place `<template>`, `<script>`, then `<style>` in that order. Make sure to put ts code in `<script>` only.
 
 ## 🚦 Frontend Logic & Event Bus
 
@@ -41,7 +46,7 @@
 - `backend/models/` — Python dataclasses (business logic, serialization)
 - `backend/db/` — TinyDB setup and helpers
 - `backend/events/` — SSE event types, broadcaster, payloads
-- `frontend/vue-app/` — Vue 3 frontend (see `src/common/`, `src/components/`, `src/layout/`)
+- `frontend/vue-app/` — Vue 3 frontend (see `src/common/`, `src/components/`, `src/layout/`) - Where tests are run from
 - `frontend/vue-app/src/common/models.ts` — TypeScript interfaces (mirror Python models)
 - `frontend/vue-app/src/common/api.ts` — API helpers, error parsing, validation
 - `frontend/vue-app/src/common/backendEvents.ts` — SSE event types and handlers