feat: migrate to Next.js for Mini App and enhance project structure

- Replaced the previous webapp with a new Mini App built using Next.js, improving performance and maintainability.
- Updated the `.gitignore` to exclude Next.js build artifacts and node modules.
- Revised documentation in `AGENTS.md`, `README.md`, and `architecture.md` to reflect the new Mini App structure and technology stack.
- Enhanced Dockerfile to support the new build process for the Next.js application.
- Updated CI workflow to build and test the Next.js application.
- Added new configuration options for the Mini App, including `MINI_APP_SHORT_NAME` for improved deep linking.
- Refactored frontend testing setup to accommodate the new structure and testing framework.
- Removed legacy webapp files and dependencies to streamline the project.

.cursor/rules/project.mdc

@@ -20,7 +20,7 @@ with a Telegram Mini App (webapp) for calendar visualization.
 ┌──────────────┐   HTTP       ┌──────────▼───────────┐
 │  Telegram    │◄────────────►│  FastAPI (api/)       │
 │  Mini App    │  initData    │  + static webapp      │
-│  (webapp/)   │  auth        └──────────┬───────────┘
+│  (webapp-next/) │  auth     └──────────┬───────────┘
 └──────────────┘                         │
                               ┌──────────▼───────────┐
                               │  SQLite + SQLAlchemy  │
@@ -31,7 +31,7 @@ with a Telegram Mini App (webapp) for calendar visualization.
 - **Bot:** python-telegram-bot v22, async polling mode.
 - **API:** FastAPI served by uvicorn in a daemon thread alongside the bot.
 - **Database:** SQLite via SQLAlchemy 2.x ORM; Alembic for migrations.
-- **Frontend:** Vanilla JS Telegram Mini App at `/app`, no framework.
+- **Frontend:** Next.js (TypeScript, Tailwind, shadcn/ui) static export at `/app`; source in `webapp-next/`.
 
 ## Key packages
 
@@ -46,7 +46,7 @@ with a Telegram Mini App (webapp) for calendar visualization.
 | `duty_teller/utils/` | Date helpers, user utilities, HTTP client |
 | `duty_teller/cache.py` | TTL caches with pattern-based invalidation |
 | `duty_teller/config.py` | Environment-based configuration |
-| `webapp/` | Telegram Mini App (HTML + JS + CSS) |
+| `webapp-next/` | Telegram Mini App (Next.js, Tailwind, shadcn/ui; build → `out/`) |
 
 ## API endpoints
 
@@ -103,7 +103,7 @@ Triggered on `v*` tags:
 ## Languages
 
 - **Backend:** Python 3.12+
-- **Frontend:** Vanilla JavaScript (ES modules, no bundler)
+- **Frontend:** Next.js (TypeScript), Tailwind CSS, shadcn/ui; Vitest for tests
 - **i18n:** Russian (default) and English
 
 ## Version control