chore: Deprecate ai.monitoring.record_token_usage()

[alexander-alderman-webb]

Description

Deprecate the function, pending removal in the upcoming major.
Inline uses of the function in integrations.

Issues

Contributes to #6894

Reminders

• Please add tests to validate your changes, and lint your code using uv run ruff.
• Add GH Issue ID & Linear ID (if applicable)
• PR title should use conventional commit style (feat:, fix:, ref:, meta:)
• For external contributors: CONTRIBUTING.md, Sentry SDK development docs, Discord community

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[github-actions]

Codecov Results 📊

✅ 133451 passed | ⏭️ 7276 skipped | Total: 140727 | Pass Rate: 94.83% | Execution Time: 460m 47s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📈 +34
Passed Tests	📈 +34
Failed Tests	—
Skipped Tests	—

All tests are passing successfully.

✅ Patch coverage is 85.71%. Project has 2593 uncovered lines.
❌ Project coverage is 90.26%. Comparing base (1f4ba26) to head (cb7a639).

Files with missing lines (6)

File	Patch %	Lines
sentry_sdk/integrations/cohere.py	66.67%	⚠️ 6 Missing and 4 partials
sentry_sdk/integrations/huggingface_hub.py	82.61%	⚠️ 4 Missing and 6 partials
sentry_sdk/integrations/litellm.py	92.31%	⚠️ 1 Missing and 4 partials
sentry_sdk/integrations/openai.py	96.15%	⚠️ 1 Missing and 3 partials
sentry_sdk/integrations/anthropic.py	100.00%	⚠️ 3 partials
sentry_sdk/ai/monitoring.py	0.00%	⚠️ 1 Missing

Coverage diff

@@            Coverage Diff             @@
##        master       #PR       +/-##
==========================================
- Coverage    90.37%    90.26%    -0.11%
==========================================
  Files          202       202         —
  Lines        26552     26625       +73
  Branches      9854      9926       +72
==========================================
+ Hits         23995     24032       +37
- Misses        2557      2593       +36
- Partials      1495      1515       +20

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[ericapisani]

These changes LGTM but warden looks to be right about huggingface_hub still using record_token_usage. Is the migration away from this there happening in a follow up?

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