[Feat] Supports Anthropic Messages count_tokens API

[chaunceyjiang]

Purpose

FIX #29915

Test Plan

curl http://localhost:8000/v1/messages/count_tokens\?beta\=true \
    -H 'Content-Type: application/json' \
    -H 'anthropic-version: 2023-06-01' \
    -H "X-Api-Key: $ANTHROPIC_API_KEY" \
    -d '{
          "messages": [
            {
              "content": "string",
              "role": "user"
            }
          ],
          "model": "my-model"
        }'

Test Result

{"input_tokens":11,"context_management":{"original_input_tokens":11}}

---

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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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• (Optional) Release notes update. If your change is user facing, please update the release notes draft in the Google Doc.

[gemini-code-assist]

Code Review

This pull request introduces a count_tokens endpoint for the Anthropic Messages API. The implementation is a good start, but I've identified a critical issue that would cause a runtime error due to a type mismatch when converting the request. Additionally, there are opportunities to improve code quality in the new API router by addressing code duplication and an inconsistent method call, which I've flagged as high-severity concerns.

[mergify]

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[chaunceyjiang]

Test:

[chaunceyjiang]

/cc @DarkLight1337 PTAL.

[mergify]

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

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

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