[Core][Hybrid allocator + connector] Support hybrid allocator + kv cache connector

[KuntaiDu]

[Core][Hybrid allocator + connector] Support hybrid allocator + kv cache connector

Checklist at the bottom is considered.

Purpose

This PR aims to support hybrid allocator + kv cache connector code path.

Design doc: link

Related to #23079
Solves #22292

Test Plan

Local correctness test passed. Will further work on instructions to let other people reproduce.

Core test logic:

        first_prompt = "Hello, how are you?" * 5000 + "Hello, my name is"
        second_prompt = [
            "Hello, how are you?" * 1000 + "Tell me a very long story",
        ]
        sampling_params = SamplingParams(temperature=0, top_p=0.95, max_tokens=10)
        print_output(llm, [first_prompt], sampling_params, "first")
        print_output(llm, ["1" + first_prompt], sampling_params, "second")
        print_output(llm, ["2" + first_prompt], sampling_params, "second")

        # Now the first request is evicted. Run this request.
        # It will trigger KV cache loading from LMCache.
        print_output(llm, second_prompt, sampling_params, "third")

Test Result

For the last request:

[2025-08-26 05:36:37,718] LMCache INFO: Reqid: 3, Total tokens 6007, LMCache hit tokens: 5888, need to load: 5888 (vllm_v1_adapter.py:1091:lmcache.integration.vllm.vllm_v1_adapter)
[2025-08-26 05:36:37,820] LMCache INFO: Retrieved 5888 tokens (vllm_v1_adapter.py:822:lmcache.integration.vllm.vllm_v1_adapter)
Processed prompts: 100%|██████████████████████████████████████████████████████████████████████████████| 1/1 [00:00<00:00,  1.26it/s, est. speed input: 7594.87 toks/s, output: 12.64 toks/s]
--------------------------------------------------
Generated text: '.\n\nOkay, here we go...\n\nOnce'
Generation took 0.80 seconds, third request done.
--------------------------------------------------
[2025-08-26 05:36:44,886] LMCache INFO: Storage manager closed. (storage_manager.py:472:lmcache.v1.storage_backend.storage_manager)
[2025-08-26 05:36:48,332] LMCache INFO: LMCacheEngine closed. (cache_engine.py:965:lmcache.v1.cache_engine)

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Essential Elements of an Effective PR Description Checklist

• 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
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model.
• (Optional) Release notes update. If your change is user facing, please update the release notes draft in the Google Doc.

[mergify]

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

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

[gemini-code-assist]

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[heheda12345]

Will take deeper look later

[mergify]

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

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

[heheda12345]

Some random idea to discuss