feat(model): add model type filtering support

- Add model_types parameter to ModelListingHandler to support filtering by model type
- Implement get_model_types endpoint in ModelQueryHandler to retrieve available model types
- Register new /api/lm/{prefix}/model-types route for model type queries
- Extend BaseModelService to handle model type filtering in queries
- Support both model_type and civitai_model_type query parameters for backward compatibility

This enables users to filter models by specific types, improving model discovery and organization capabilities.

tests/services/test_base_model_service.py

@@ -776,6 +776,67 @@ def test_model_filter_set_supports_legacy_tag_arrays():
     assert [item["model_name"] for item in result] == ["StyleOnly", "StyleAnime"]
 
 
+def test_model_filter_set_filters_by_model_types():
+    settings = StubSettings({})
+    filter_set = ModelFilterSet(settings)
+    data = [
+        {"model_name": "LoConModel", "civitai": {"model": {"type": "LoCon"}}},
+        {"model_name": "LoRaModel", "civitai": {"model": {"type": "LoRa"}}},
+    ]
+
+    criteria = FilterCriteria(model_types=["locon"])
+    result = filter_set.apply(data, criteria)
+
+    assert [item["model_name"] for item in result] == ["LoConModel"]
+
+
+def test_model_filter_set_defaults_missing_model_type_to_lora():
+    settings = StubSettings({})
+    filter_set = ModelFilterSet(settings)
+    data = [
+        {"model_name": "DefaultModel"},
+        {"model_name": "CheckpointModel", "civitai": {"model": {"type": "checkpoint"}}},
+    ]
+
+    criteria = FilterCriteria(model_types=["lora"])
+    result = filter_set.apply(data, criteria)
+
+    assert [item["model_name"] for item in result] == ["DefaultModel"]
+
+
+@pytest.mark.asyncio
+async def test_get_model_types_counts_and_limits():
+    raw_data = [
+        {"civitai": {"model": {"type": "LoRa"}}},
+        {"model_type": "LoRa"},
+        {"civitai": {"model": {"type": "LoCon"}}},
+        {},
+    ]
+
+    class CacheStub:
+        def __init__(self, raw_data):
+            self.raw_data = raw_data
+
+    class ScannerStub:
+        def __init__(self, cache):
+            self._cache = cache
+
+        async def get_cached_data(self, *_, **__):
+            return self._cache
+
+    cache = CacheStub(raw_data)
+    scanner = ScannerStub(cache)
+    service = DummyService(
+        model_type="stub",
+        scanner=scanner,
+        metadata_class=BaseModelMetadata,
+    )
+
+    types = await service.get_model_types(limit=1)
+
+    assert types == [{"type": "LoRa", "count": 2}]
+
+
 @pytest.mark.asyncio
 @pytest.mark.parametrize(
     "service_cls, extra_fields",