feat: restructure test infrastructure with unit/integration/system separation

Test Organization:
- Create tests/unit/, tests/integration/, tests/system/ directories
- Move existing tests into appropriate categories
- Add pytest markers (@pytest.mark.unit, @pytest.mark.integration)

Shared Fixtures:
- Create conftest.py with SQLite engine (for unit tests)
- Add PostgreSQL session fixture with transaction rollback
- Add TestClient fixture for API tests

Configuration:
- Update pyproject.toml with asyncio_mode=auto
- Add test markers and default addopts
- Add aiosqlite dependency for SQLite support

E2E Testing:
- Initialize Playwright in e2e/ directory
- Add playwright.config.ts
- Create login flow E2E test

Build:
- Add test-unit, test-integration, test-system, test-e2e to Makefile
- Update test target to run all categories
- Add testing documentation to README

Note: Some tests have import issues due to missing python-jose
package in dev environment. This needs to be addressed separately.

Makefile

@@ -1,18 +1,22 @@
-.PHONY: help up down logs migrate test lint clean build
+.PHONY: help up down logs migrate test test-unit test-integration test-system test-e2e lint clean build
 
 # Default target
 help:
 	@echo "Headquarter Development Commands"
 	@echo "================================"
-	@echo "make up       - Start all services"
-	@echo "make down     - Stop all services"
-	@echo "make logs     - View service logs"
-	@echo "make migrate  - Run database migrations"
-	@echo "make test     - Run test suites"
-	@echo "make lint     - Run linting"
-	@echo "make build    - Build all Docker images"
-	@echo "make clean    - Remove containers and volumes"
-	@echo "make shell    - Open shell in API container"
+	@echo "make up           - Start all services"
+	@echo "make down         - Stop all services"
+	@echo "make logs         - View service logs"
+	@echo "make migrate      - Run database migrations"
+	@echo "make test         - Run all test suites"
+	@echo "make test-unit    - Run unit tests only"
+	@echo "make test-integration - Run integration tests only"
+	@echo "make test-system  - Run system tests only"
+	@echo "make test-e2e     - Run E2E tests (Playwright)"
+	@echo "make lint         - Run linting"
+	@echo "make build        - Build all Docker images"
+	@echo "make clean        - Remove containers and volumes"
+	@echo "make shell        - Open shell in API container"
 
 # Start services
 up:
@@ -49,10 +53,26 @@ migrate:
 migration:
 	docker compose exec api alembic revision --autogenerate -m "$(message)"
 
-# Run tests
+# Run all tests
 test:
 	docker compose exec api pytest -v
 
+# Run unit tests only (fast, no external dependencies)
+test-unit:
+	docker compose exec api pytest -v -m unit tests/unit/
+
+# Run integration tests only (requires database)
+test-integration:
+	docker compose exec api pytest -v -m integration tests/integration/
+
+# Run system tests only (full stack)
+test-system:
+	docker compose exec api pytest -v -m system tests/system/
+
+# Run E2E tests (requires full application stack)
+test-e2e:
+	cd e2e && npx playwright test
+
 # Run linting
 lint:
 	docker compose exec api ruff check .