feat: add Cortecs AI as OpenAI-compatible provider

- Add cortecs config to providers.json (base_url + api_key_env)
- Add cortecs to provider_endpoints_support.json (chat_completions only)

Follows the minimal JSON-configured provider pattern. The JSON
provider registry automatically handles routing without needing
manual entries in constants.py or types/utils.py.

litellm/llms/openai_like/providers.json

@@ -106,5 +106,9 @@
     "base_url": "https://aihubmix.com/v1",
     "api_key_env": "AIHUBMIX_API_KEY",
     "api_base_env": "AIHUBMIX_API_BASE"
+  },
+  "cortecs": {
+    "base_url": "https://api.cortecs.ai/v1",
+    "api_key_env": "CORTECS_API_KEY"
   }
 }

litellm/provider_endpoints_support_backup.json

@@ -474,6 +474,23 @@
         "a2a": false
       }
     },
+    "cortecs": {
+      "display_name": "Cortecs AI (`cortecs`)",
+      "url": "https://docs.litellm.ai/docs/providers/cortecs",
+      "endpoints": {
+        "chat_completions": true,
+        "messages": false,
+        "responses": false,
+        "embeddings": false,
+        "image_generations": false,
+        "audio_transcriptions": false,
+        "audio_speech": false,
+        "moderations": false,
+        "batches": false,
+        "rerank": false,
+        "a2a": false
+      }
+    },
     "clarifai": {
       "display_name": "Clarifai (`clarifai`)",
       "url": "https://docs.litellm.ai/docs/providers/clarifai",

provider_endpoints_support.json

@@ -509,6 +509,23 @@
         "a2a": false
       }
     },
+    "cortecs": {
+      "display_name": "Cortecs AI (`cortecs`)",
+      "url": "https://docs.litellm.ai/docs/providers/cortecs",
+      "endpoints": {
+        "chat_completions": true,
+        "messages": false,
+        "responses": false,
+        "embeddings": false,
+        "image_generations": false,
+        "audio_transcriptions": false,
+        "audio_speech": false,
+        "moderations": false,
+        "batches": false,
+        "rerank": false,
+        "a2a": false
+      }
+    },
     "clarifai": {
       "display_name": "Clarifai (`clarifai`)",
       "url": "https://docs.litellm.ai/docs/providers/clarifai",