litellm proxy instrumentation

[ncybul]

Checklist

• PR author has checked that all the criteria below are met
• The PR description includes an overview of the change
• The PR description articulates the motivation for the change
• The change includes tests OR the PR description describes a testing strategy
• The PR description notes risks associated with the change, if any
• Newly-added code is easy to change
• The change follows the library release note guidelines
• The change includes or references documentation updates if necessary
• Backport labels are set (if applicable)

Reviewer Checklist

• Reviewer has checked that all the criteria below are met
• Title is accurate
• All changes are related to the pull request's stated goal
• Avoids breaking API changes
• Testing strategy adequately addresses listed risks
• Newly-added code is easy to change
• Release note makes sense to a user of the library
• If necessary, author has acknowledged and discussed the performance implications of this PR as reported in the benchmarks PR comment
• Backport labels are set in a manner that is consistent with the release branch maintenance policy

[github-actions]

CODEOWNERS have been resolved as:

ddtrace/contrib/internal/litellm/patch.py                               @DataDog/apm-core-python @DataDog/apm-idm-python

[github-actions]

Bootstrap import analysis

Comparison of import times between this PR and base.

Summary

The average import time from this PR is: 231 ± 2 ms.

The average import time from base is: 233 ± 2 ms.

The import time difference between this PR and base is: -2.22 ± 0.08 ms.

Import time breakdown

The following import paths have shrunk:

ddtrace.auto 1.988 ms (0.86%)

ddtrace.bootstrap.sitecustomize 1.324 ms (0.57%)

ddtrace.bootstrap.preload 1.324 ms (0.57%)

ddtrace.internal.products 1.324 ms (0.57%)

ddtrace.internal.remoteconfig.client 0.630 ms (0.27%)

ddtrace 0.664 ms (0.29%)