fix(llmobs): fix input tokens counting for anthropic

[lievan]

When prompt caching is used in anthropic, the number of input tokens returned in the usage field is the number of non cached tokens, not the total number of tokens sent to the model (what we expect in datadog)

This pr fixes this by setting input tokens to the total number of input tokens (cache read + cache write + input tokens)

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:

releasenotes/notes/fix-anthropic-input-tokens-unified-calculation-a1b2c3d4e5f6g7h8.yaml  @DataDog/apm-python
ddtrace/llmobs/_integrations/anthropic.py                               @DataDog/ml-observability
tests/contrib/anthropic/test_anthropic_llmobs.py                        @DataDog/ml-observability

[github-actions]

Bootstrap import analysis

Comparison of import times between this PR and base.

Summary

The average import time from this PR is: 275 ± 3 ms.

The average import time from base is: 280 ± 3 ms.

The import time difference between this PR and base is: -4.9 ± 0.1 ms.

Import time breakdown

The following import paths have shrunk:

ddtrace.auto 2.259 ms (0.82%)

ddtrace.bootstrap.sitecustomize 1.560 ms (0.57%)

ddtrace.bootstrap.preload 1.560 ms (0.57%)

ddtrace.internal.remoteconfig.client 0.704 ms (0.26%)

ddtrace.debugging._import 0.014 ms (0.01%)

ddtrace.debugging._function.discovery 0.014 ms (0.01%)

ddtrace.debugging._function 0.014 ms (0.01%)

ddtrace 0.699 ms (0.25%)

ddtrace.internal._unpatched 0.032 ms (0.01%)

json 0.032 ms (0.01%)

json.decoder 0.032 ms (0.01%)

re 0.032 ms (0.01%)

enum 0.032 ms (0.01%)

types 0.032 ms (0.01%)

ddtrace.settings._config 0.016 ms (0.01%)

ddtrace.internal.schema 0.016 ms (0.01%)

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-07-15 03:55:42

Comparing candidate commit 14de3cf in PR branch evan.li/fix-ant-tokens with baseline commit c8d1431 in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 424 metrics, 2 unstable metrics.