fix: address pre-merge review findings — stale identity strings, pyright error, fragile test path, formatting, README accuracy

Required fixes:
- main.py: update module docstring, startup comment, and FastAPI title from
  'tmux-web coordinator' / 'coordinator service' → 'muxplex' (4 locations)
- test_api.py: replace hasattr/BaseRoute pattern with isinstance(r, (APIRoute,
  APIWebSocketRoute)) to satisfy pyright (union-attr error eliminated)

Recommendations applied:
- test_api.py + test_cli.py: auto-formatted with ruff (blank-line normalisation)
- test_cli.py: replace exec(Path('muxplex/__main__.py').read_text()) with
  importlib.util.find_spec() to obtain the absolute path — no longer assumes
  pytest is invoked from a specific working directory
- README.md: fix architecture table — WebSocket proxy moved from ttyd.py
  description to main.py; ttyd.py now correctly described as lifecycle only

All 178 tests pass; python_check clean (0 errors, 0 warnings).

README.md

@@ -171,10 +171,10 @@ muxplex/
     ├── __init__.py
     ├── __main__.py         # `python -m muxplex` entry point
     ├── cli.py              # CLI argument parsing and `install-service` subcommand
-    ├── main.py             # FastAPI app factory and route registration
+    ├── main.py             # FastAPI app: session API, bell hooks, WebSocket proxy to ttyd, static frontend
     ├── sessions.py         # tmux session discovery and snapshot capture
     ├── bells.py            # Bell/activity notification tracking
-    ├── ttyd.py             # ttyd process lifecycle management and WebSocket proxy
+    ├── ttyd.py             # ttyd process lifecycle management (spawn, kill, PID tracking)
     ├── state.py            # Shared in-process state (sessions, bells, ttyd)
     ├── frontend/           # Static frontend assets (served as package data)
     │   ├── index.html

muxplex/main.py

@@ -1,7 +1,7 @@
 """
-FastAPI coordinator application for tmux-web.
+muxplex — FastAPI application for the tmux session dashboard.
 
-Entry point for the coordinator service. Exposes:
+Entry point for the muxplex server. Exposes:
     GET /health  →  {"status": "ok"}
 
 Background poll loop reconciles tmux session state every POLL_INTERVAL seconds.
@@ -138,7 +138,7 @@ async def _poll_loop() -> None:
 async def lifespan(app: FastAPI):
     global _poll_task
 
-    # Startup: kill any orphaned ttyd from a previous coordinator run, then
+    # Startup: kill any orphaned ttyd from a previous muxplex run, then
     # start the background poll loop.
     await kill_orphan_ttyd()
     _poll_task = asyncio.create_task(_poll_loop())
@@ -170,7 +170,7 @@ async def lifespan(app: FastAPI):
 # App
 # ---------------------------------------------------------------------------
 
-app = FastAPI(title="tmux-web coordinator", version="0.1.0", lifespan=lifespan)
+app = FastAPI(title="muxplex", version="0.1.0", lifespan=lifespan)
 
 
 # ---------------------------------------------------------------------------

muxplex/tests/test_api.py

@@ -1,5 +1,5 @@
 """
-Tests for coordinator/main.py — FastAPI skeleton, lifespan, /health endpoint.
+Tests for muxplex/main.py — FastAPI skeleton, lifespan, /health endpoint.
 """
 
 import pytest
@@ -149,9 +149,7 @@ def test_patch_state_ignores_unknown_fields(client):
 def test_get_sessions_returns_list(client, monkeypatch):
     """GET /api/sessions must return a JSON list."""
     monkeypatch.setattr("muxplex.main.get_session_list", lambda: ["alpha"])
-    monkeypatch.setattr(
-        "muxplex.main.get_snapshots", lambda: {"alpha": "some text"}
-    )
+    monkeypatch.setattr("muxplex.main.get_snapshots", lambda: {"alpha": "some text"})
 
     response = client.get("/api/sessions")
     assert response.status_code == 200
@@ -210,9 +208,7 @@ def test_get_sessions_includes_bell_state(client, monkeypatch):
     from muxplex.state import save_state
 
     monkeypatch.setattr("muxplex.main.get_session_list", lambda: ["delta"])
-    monkeypatch.setattr(
-        "muxplex.main.get_snapshots", lambda: {"delta": "pane text"}
-    )
+    monkeypatch.setattr("muxplex.main.get_snapshots", lambda: {"delta": "pane text"})
     save_state(
         {
             "active_session": None,
@@ -647,9 +643,13 @@ def test_api_routes_not_shadowed(client):
 
 def test_terminal_ws_route_exists():
     """The app must have a WebSocket route registered at /terminal/ws."""
+    from fastapi.routing import APIRoute, APIWebSocketRoute
+
     from muxplex.main import app
+
     ws_routes = [
-        r for r in app.routes
-        if hasattr(r, "path") and r.path == "/terminal/ws"
+        r
+        for r in app.routes
+        if isinstance(r, (APIRoute, APIWebSocketRoute)) and r.path == "/terminal/ws"
     ]
     assert len(ws_routes) == 1, "Expected exactly one /terminal/ws route"

muxplex/tests/test_cli.py

@@ -4,7 +4,6 @@ from pathlib import Path
 from unittest.mock import patch
 
 
-
 def test_cli_module_importable():
     """muxplex.cli must be importable."""
     from muxplex.cli import main  # noqa: F401
@@ -87,12 +86,12 @@ def test_install_service_system_mode_target(tmp_path, monkeypatch):
 
 def test_dunder_main_calls_main():
     """python -m muxplex must call cli.main()."""
-    with patch("muxplex.cli.main") as mock_main:
-        # Simulate `python -m muxplex` by exec'ing __main__.py
-        import muxplex.__main__  # noqa: F401
+    import importlib.util
 
-        # The import itself calls main() at module level
-        # Re-exec to test:
-        mock_main.reset_mock()
-        exec(Path("muxplex/__main__.py").read_text())
+    # Locate __main__.py without executing it (find_spec does not import)
+    spec = importlib.util.find_spec("muxplex.__main__")
+    assert spec is not None and spec.origin is not None
+
+    with patch("muxplex.cli.main") as mock_main:
+        exec(Path(spec.origin).read_text())  # noqa: S102
         mock_main.assert_called_once()