Add test suite (63 tests) and CI workflow, fix Settings API bugs

Test suite covering all three layers:

Python backend (25 tests):
- AppController: state machine, start/stop, callbacks, settings reload
- API server: REST endpoints, config CRUD, status, devices
- Config: dot-notation get/set, persistence, nested paths
- Main headless: ready event port format validation

Svelte frontend (14 tests via Vitest):
- Backend store: exported properties/methods, port derivation, URLs
- Config store: method names (fetchConfig not loadConfig), defaults
- Transcriptions store: add/clear/plaintext
- File extension regression: ensures $state runes only in .svelte.ts

Rust sidecar (24 tests via cargo test):
- Platform/arch detection, asset name construction
- Ready event deserialization (with extra fields tolerance)
- Path construction, version read/write, old version cleanup
- Zip extraction, SidecarManager lifecycle

CI workflow (.gitea/workflows/test.yml):
- Runs on push to main and PRs
- Three parallel jobs: Python, Frontend, Rust

Also fixes three bugs found during test planning:
- Settings: /api/check-updates -> GET /api/check-update
- Settings: /api/remote/login -> /api/login
- Settings: /api/remote/register -> /api/register

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/tests/test_main_headless.py

@@ -0,0 +1,56 @@
+"""Tests for backend.main_headless ready-event JSON format."""
+
+import sys
+from pathlib import Path
+
+import pytest
+
+# Ensure project root is on path
+project_root = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(project_root))
+
+
+def test_ready_event_reports_api_port_not_obs_port():
+    """The ready JSON printed by main_headless must set ``port`` to
+    ``obs_port + 1`` (the API port), not the OBS display port.
+
+    From main_headless.py::
+
+        obs_port = controller.actual_web_port or args.port
+        api_port = obs_port + 1
+
+        print(json.dumps({
+            "event": "ready",
+            "port": api_port,
+            "obs_port": obs_port,
+        }), flush=True)
+
+    We verify this contract by reading the source and checking the
+    structure directly (running main() would start a real server).
+    """
+    import ast
+    import textwrap
+
+    source_path = project_root / "backend" / "main_headless.py"
+    source = source_path.read_text()
+
+    # Verify the key relationships exist in the source:
+    # 1. api_port = obs_port + 1
+    assert "api_port = obs_port + 1" in source, (
+        "Expected `api_port = obs_port + 1` in main_headless.py"
+    )
+
+    # 2. The ready event JSON uses api_port for "port", not obs_port
+    assert '"port": api_port' in source or "'port': api_port" in source, (
+        "The ready event should report api_port as 'port'"
+    )
+
+    # 3. obs_port is also included separately
+    assert '"obs_port": obs_port' in source or "'obs_port': obs_port" in source, (
+        "The ready event should also include 'obs_port'"
+    )
+
+    # 4. Verify the event name
+    assert '"event": "ready"' in source or "'event': 'ready'" in source, (
+        "The ready event should have event='ready'"
+    )