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.

openspec/changes/test-infrastructure-improvements/specs/e2e-testing/spec.md

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+## ADDED Requirements
+
+### Requirement: E2E Test Framework
+
+The system SHALL provide end-to-end tests using Playwright.
+
+#### Scenario: Test setup
+- GIVEN the e2e test directory
+- THEN `e2e/` SHALL contain Playwright configuration
+- AND tests SHALL run against the full application stack
+
+#### Scenario: Critical user journeys
+- GIVEN the e2e test suite
+- THEN it SHALL test:
+  - User login flow
+  - Project creation and listing
+  - SSH key generation
+
+#### Scenario: Test environment
+- GIVEN e2e tests are running
+- THEN they SHALL use a dedicated test database
+- AND tests SHALL clean up data after completion
+
+### Requirement: Test Commands
+
+The system SHALL provide Makefile targets for running different test categories.
+
+#### Scenario: Make targets
+- GIVEN the Makefile
+- THEN these targets SHALL exist:
+  - `make test-unit` - Run unit tests only
+  - `make test-integration` - Run integration tests only
+  - `make test-system` - Run system tests only
+  - `make test-e2e` - Run Playwright E2E tests
+  - `make test` - Run all backend tests

openspec/changes/test-infrastructure-improvements/specs/test-isolation/spec.md

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+## ADDED Requirements
+
+### Requirement: Shared Test Fixtures
+
+The system SHALL provide shared fixtures in `conftest.py` for common test needs.
+
+#### Scenario: Database session fixture
+- GIVEN an integration test
+- WHEN using the `db_session` fixture
+- THEN it SHALL provide an async SQLAlchemy session
+- AND the session SHALL use transaction rollback for isolation
+
+#### Scenario: Test client fixture
+- GIVEN an API integration test
+- WHEN using the `client` fixture
+- THEN it SHALL provide an authenticated TestClient instance
+- AND the client SHALL have valid access and refresh tokens
+
+#### Scenario: SQLite unit test database
+- GIVEN a unit test
+- WHEN the test uses the `db_engine` fixture
+- THEN it SHALL provide an in-memory SQLite engine
+- AND no PostgreSQL connection SHALL be required
+
+### Requirement: Transaction Isolation
+
+The system SHALL ensure integration tests don't pollute the database.
+
+#### Scenario: Rollback after test
+- GIVEN an integration test creates data
+- WHEN the test completes
+- THEN all database changes SHALL be rolled back
+- AND subsequent tests SHALL see a clean database state
+
+#### Scenario: Parallel test safety
+- GIVEN multiple integration tests run concurrently
+- WHEN each test uses transaction isolation
+- THEN tests SHALL not interfere with each other

openspec/changes/test-infrastructure-improvements/specs/test-organization/spec.md

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+## ADDED Requirements
+
+### Requirement: Test Directory Structure
+
+The system SHALL organize tests into unit, integration, and system directories.
+
+#### Scenario: Directory layout
+- GIVEN the backend test suite
+- THEN `apps/api/tests/` SHALL contain:
+  - `unit/` - Pure logic tests with no external dependencies
+  - `integration/` - API endpoint tests with database
+  - `system/` - Full stack tests with external services
+
+#### Scenario: Running selective tests
+- GIVEN the test suite is organized
+- WHEN running `pytest -m unit`
+- THEN only unit tests SHALL execute
+- AND WHEN running `pytest -m integration`
+- THEN only integration tests SHALL execute
+
+### Requirement: Test Markers
+
+The system SHALL provide pytest markers for each test category.
+
+#### Scenario: Marker registration
+- GIVEN pytest configuration
+- THEN `pyproject.toml` SHALL register markers:
+  - `unit` - Fast tests with no external dependencies
+  - `integration` - Tests with database and external services
+  - `system` - End-to-end tests of the full stack
+
+#### Scenario: Marker usage
+- GIVEN a test file
+- THEN unit tests SHALL be marked with `@pytest.mark.unit`
+- AND integration tests SHALL be marked with `@pytest.mark.integration`
+- AND system tests SHALL be marked with `@pytest.mark.system`