feat: Implement In-Tree Embedding Similarity Matching

[Sophie8]

What type of PR is this?

• [Prompt Classification] Implement In-Tree Embedding Similarity Matching

What this PR does / why we need it:
Implement the embedding based in tree classification based on the design roadmap:

• Reuse existing candle-binding embedding models
• Embedding similarity scoring
• Configurable thresholds per category (e.g. category A: 80%, category B: 60%)
• Support mean/max/any aggregation methods to find the best match

Which issue(s) this PR fixes:

Feature # 336

Release Notes: Yes/No

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[github-actions]

👥 vLLM Semantic Team Notification

The following members have been identified for the changed files in this PR and have been automatically assigned:

📁 website

Owners: @Xunzhuo, @rootfs, @yuluo-yx
Files changed:

• website/src/components/ScrollToTop/index.tsx
• website/src/components/ScrollToTop/styles.module.css
• website/src/theme/Root.tsx

📁 src

Owners: @rootfs, @Xunzhuo, @wangchen615
Files changed:

• src/semantic-router/pkg/api/server.go

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🎉 Thanks for your contributions!

This comment was automatically generated based on the OWNER files in the repository.

[Xunzhuo]

can you design the API first?

[Sophie8]

can you design the API first?

sure.
Todos:

1. The PR will be refactored after embedding model at candle binding is finalized: feat: add embedding model continuous batching scheduler #564
2. design doc for API, benchmarks and unit tests to be added

[Xunzhuo]

fixes: #366

[Sophie8]

closing this draft PR as changes are refactored and migrated to #606 for better code structure.