Add renderer-based prompt processing for embedding and classification endpoints

[sfeng33]

Purpose

Refactors the embedding and classification endpoints to use the new CompletionRenderer for consistent prompt processing across all API endpoints.

Issue: #22880
Previous PR: #24010

Test Plan

1. Unit test

pytest tests/entrypoints/test_renderer.py -v

2. Manual test

# Embedding endpoint
python -m vllm.entrypoints.openai.api_server \
      --model BAAI/bge-base-en-v1.5 \
      --port 8000

curl -X POST http://localhost:8000/v1/embeddings \
-H "Content-Type: application/json" \
-d '{
  "model": "BAAI/bge-base-en-v1.5",
  "input": "Hello this is a test sentence for embeddings"
}'

# Classification endpoint
python -m vllm.entrypoints.openai.api_server \
    --model nie3e/sentiment-polish-gpt2-small \
    --port 8000 


curl http://localhost:8000/classify \
  -H "Content-Type: application/json" \
  -d '{
    "input": "hello",
    "model": "nie3e/sentiment-polish-gpt2-small"
  }'

[DarkLight1337]

LGTM if tests pass. However CI is broken right now so let's try merging after that's fixed

[sfeng33]

Sounds good, thanks for the review!