[Rust] Rename mem-cache to sglang-radix-tree

[Jialin]

Motivation

The Rust TreeCore crate was introduced as mem-cache, which is broader than the implementation it contains and does not follow the naming convention of the other SGLang Rust crates.

Rename it to sglang-radix-tree so its ownership and purpose are explicit before follow-up feature work lands.

Modifications

• Rename the standalone crate directory from rust/mem-cache to rust/sglang-radix-tree.
• Rename the Cargo package from mem_cache to sglang-radix-tree.
• Update Cargo workspace metadata, extension discovery, pre-commit commands, CI build paths, documentation, and the registered native-test entry point.
• Keep the existing Python and shared-library ABI names unchanged:
  • sglang.srt.mem_cache.rust_tree_core.mem_cache
  • mem_cache_inspection
  • libmem_cache.so

All moved Rust implementation and test sources are byte-identical; this PR changes crate identity and build wiring only.

Accuracy Tests

Not applicable: this PR does not change model execution or radix-tree behavior.

Validation performed:

• Native Rust suite: 831 passed, 1 ignored.
• Rust extension discovery suite: 14 passed.
• Production and inspection extensions built and imported under the existing Python module names.
• cargo metadata --locked passed for both the standalone crate and root Rust workspace.
• All moved Rust implementation/test files and the compatibility header were verified byte-for-byte against their pre-rename contents.

Speed Tests and Profiling

Not applicable: no runtime implementation changed, and the generated extension/library ABI remains unchanged.

Checklist

• Format your code according to the Format code with pre-commit.
• Add unit tests according to the Run and add unit tests.
• Update documentation according to Write documentations.
• Provide accuracy and speed benchmark results according to Test the accuracy and Benchmark the speed. (Not applicable for this rename-only change.)
• Follow the SGLang code style guidance.

Review and Merge Process

1. Ping Merge Oncalls to start the process. See the PR Merge Process.
2. Get approvals from CODEOWNERS and other reviewers.
3. Trigger CI tests with comments or contact authorized users to do so.
   • Common commands include /tag-and-rerun-ci, /tag-run-ci-label, /rerun-failed-ci
4. After green CI and required approvals, ask Merge Oncalls or people with Write permission to merge the PR.

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CI States

Latest PR Test (Base): ✅ Run #33430010718
Latest PR Test (Extra): ✅ Run #33431372202
Latest PR Test (AMD ROCm 7.2): ❌ Run #33430010739

[Jialin]

/run-failed-ci

[Jialin]

/rerun-failed-ci

• 08/31 8:18PM: AssertionError: avg_kl_div=0.106299891739351 > threshold=0.1 for Qwen/Qwen3-Next-80B-A3B-Instruct test_input_output_logprobs_match_prefill_cache_hit_helper