[Docs] Sync docs_new with legacy docs and update migration redirects (#23337)

Co-authored-by: Mingyi <wisclmy0611@gmail.com>

docs_new/docs/supported-models.mdx

@@ -13,7 +13,7 @@ SGLang supports model families across text generation, retrieval, and reward wor
     title="Large language models"
     mode="card"
     className="max-w-sm mx-auto"
-    href="./supported-models/large-language-models"
+    href="./supported-models/generative_models"
     img="/cards/LLM-card.png"
   >
     Production-tuned Llama and Qwen families validated for high-throughput
@@ -23,7 +23,7 @@ SGLang supports model families across text generation, retrieval, and reward wor
     title="Vision language models"
     mode="card"
     className="max-w-sm mx-auto"
-    href="./supported-models/vision-language-models"
+    href="./supported-models/multimodal_language_models"
     img="/cards/VLM-card.png"
   >
     Vision-text hybrids that stay responsive on multi-GPU setups.
@@ -47,7 +47,7 @@ SGLang supports model families across text generation, retrieval, and reward wor
     title="Embedding models"
     mode="card"
     className="max-w-sm mx-auto"
-    href="./supported-models/embedding-models"
+    href="./supported-models/embedding_models"
     img="/cards/Embedding-card.png"
   >
     Dense and sparse embeddings optimized with FlashInfer kernels.
@@ -56,7 +56,7 @@ SGLang supports model families across text generation, retrieval, and reward wor
     title="Rerank models"
     mode="card"
     className="max-w-sm mx-auto"
-    href="./supported-models/rerank-models"
+    href="./supported-models/rerank_models"
     img="/cards/Rerank-card.png"
   >
     Low-latency rerankers for multi-stage retrieval pipelines.
@@ -65,7 +65,7 @@ SGLang supports model families across text generation, retrieval, and reward wor
     title="Classification models"
     mode="card"
     className="max-w-sm mx-auto"
-    href="./supported-models/classification-models"
+    href="./supported-models/classify_models"
     img="/cards/Classification-card.png"
   >
     Lightweight classifiers covering safety, intent, and context filters.
@@ -79,7 +79,7 @@ SGLang supports model families across text generation, retrieval, and reward wor
     title="Reward models"
     mode="card"
     className="max-w-sm mx-auto"
-    href="./supported-models/reward-models"
+    href="./supported-models/reward_models"
     img="/cards/Reward-card.png"
   >
     RLHF and reward scoring pipelines optimized for production latency.