[Frontend] Resettle pooling entrypoints

[noooop]

Purpose

Currently, we have two entrypoints refactoring plans.

• [Refactor] [1/N] to simplify the vLLM serving architecture #28040 following [RFC]: Router Registry & Plugin System for vLLM Online Serving #28218
• [Frontend][Renderer] Refactor score API #28631 following [Renderer] Merge OpenAIServing._preprocess_* with Processor.process_inputs #23873 [RFC]: Unified Input Formatting and Processing via Renderer #22880

Merge this PR first, hoping to reduce conflicts.

├─pooling
│  ├─classify
│  ├─embed
│  ├─pooling
│  ├─score
│  │  ├─api_router
│  │  ├─protocol
│  │  └─serving

Test Plan

pytest tests/entrypoints/pooling/

Test Result

pass

---

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• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
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[mergify]

Documentation preview: https://vllm--29634.org.readthedocs.build/en/29634/

[mergify]

This pull request has merge conflicts that must be resolved before it can be
merged. Please rebase the PR, @noooop.

https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/syncing-a-fork