Update backend status handling and improve user notifications

- Enhanced documentation to clarify the transition from 'Idle' to 'ready (running)' for backend states, improving user understanding of system readiness.
- Updated logging messages in the notification system to reflect the new backend status terminology, ensuring accurate feedback during operations.
- Refined access link collection logic to better handle tunneled and non-tunneled scenarios, enhancing user experience.
- Improved tests to validate the new backend status handling and ensure accurate reporting of access links and notifications.

tests/test_hold_killer.py

@@ -76,6 +76,77 @@ def test_classify_busy_from_status(monkeypatch):
     assert "idle" in detail
 
 
+def test_classify_running_without_queue_not_busy(monkeypatch):
+    """SwarmUI 'running' = ready; empty queue → idle-killer may stop GPU."""
+    mod = _load_remote()
+
+    class FakeResp:
+        def __init__(self, payload):
+            self._payload = payload
+
+        def read(self):
+            import json
+
+            return json.dumps(self._payload).encode()
+
+        def __enter__(self):
+            return self
+
+        def __exit__(self, *args):
+            return False
+
+    def fake_urlopen(req, timeout=0, context=None):
+        url = getattr(req, "full_url", None) or req.get_full_url()
+        if "GetNewSession" in url:
+            return FakeResp({"session_id": "abc"})
+        return FakeResp(
+            {
+                "status": {"waiting_gens": 0, "live_gens": 0, "loading_models": 0},
+                "backend_status": {"status": "running", "any_loading": False},
+            }
+        )
+
+    monkeypatch.setattr(mod.urllib.request, "urlopen", fake_urlopen)
+    busy, detail = mod.swarm_busy("http://127.0.0.1:7801")
+    assert busy is False
+    assert "running" in detail
+
+
+def test_classify_loading_is_busy(monkeypatch):
+    mod = _load_remote()
+
+    class FakeResp:
+        def __init__(self, payload):
+            self._payload = payload
+
+        def read(self):
+            import json
+
+            return json.dumps(self._payload).encode()
+
+        def __enter__(self):
+            return self
+
+        def __exit__(self, *args):
+            return False
+
+    def fake_urlopen(req, timeout=0, context=None):
+        url = getattr(req, "full_url", None) or req.get_full_url()
+        if "GetNewSession" in url:
+            return FakeResp({"session_id": "abc"})
+        return FakeResp(
+            {
+                "status": {"waiting_gens": 0, "live_gens": 0, "loading_models": 0},
+                "backend_status": {"status": "loading", "any_loading": True},
+            }
+        )
+
+    monkeypatch.setattr(mod.urllib.request, "urlopen", fake_urlopen)
+    busy, detail = mod.swarm_busy("http://127.0.0.1:7801")
+    assert busy is True
+    assert "loading" in detail
+
+
 def test_classify_busy_queue(monkeypatch):
     mod = _load_remote()