feat: add Plug tracing header context

[dustinbyrne]

💡 Motivation and Context

Propagate PostHog browser tracing context through the Elixir Plug integration so backend events and exception captures can be associated with the frontend distinct ID and session.

💚 How did you test it?

• mix test test/posthog/integrations/plug_test.exs
• mix test
• Manual temporary ExUnit check for tracing headers flowing into normal capture and Bandit exception capture

📝 Checklist

• I reviewed the submitted code.
• I added tests to verify the changes.
• I updated the docs if needed.
• No breaking change or entry added to the changelog.

If releasing new changes

• Ran sampo add to generate a changeset file
• Added the release label to the PR

[github-actions]

posthog-elixir Compliance Report

Date: 2026-04-28 17:20:19 UTC
Duration: 211ms

⚠️ Some Tests Failed

0/1 tests passed, 1 failed

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Feature_Flags Tests

⚠️ 0/1 tests passed, 1 failed

View Details

Test	Status	Duration
Request Payload.Request With Person Properties Device Id	❌	7ms

Failures

request_payload.request_with_person_properties_device_id

404, message='Not Found', url='http://sdk-adapter:8080/get_feature_flag'

[dustinbyrne]

These are derived from how we're currently sanitizing tracing headers in Django