docs: register synthorai in provider_endpoints_support.json

code-quality fails with 'Found 1 undocumented openai_like providers:
synthorai'. check_provider_folders_documented.py requires an entry here
for anything listed in llms/openai_like/providers.json.

Inserted as text rather than re-serialising the file: it contains
charity_engine twice, so a json round-trip drops the first occurrence.

Endpoint flags come from the catalog's category counts, not from probing -
auth sits on the /v1 prefix so unrouted paths return 401 too. No embedding
or rerank models exist, so those are false.

provider_endpoints_support.json

@@ -509,6 +509,24 @@
         "a2a": false
       }
     },
+    "synthorai": {
+      "display_name": "Synthorai (`synthorai`)",
+      "url": "https://docs.litellm.ai/docs/providers/synthorai",
+      "endpoints": {
+        "chat_completions": true,
+        "messages": true,
+        "responses": true,
+        "embeddings": false,
+        "image_generations": true,
+        "audio_transcriptions": true,
+        "audio_speech": true,
+        "moderations": false,
+        "batches": false,
+        "rerank": false,
+        "a2a": false,
+        "interactions": false
+      }
+    },
     "clarifai": {
       "display_name": "Clarifai (`clarifai`)",
       "url": "https://docs.litellm.ai/docs/providers/clarifai",