test(ai): Add E2E Playwright tests

[Twixes]

Problem

We had to revert #35070 due to an issue no unit or integration test caught. We're entirely missing E2E coverage of PostHog AI.

Changes

Adding basic tests to ensure PostHog AI's integrity end-to-end.

[greptile-apps]

_{15 files reviewed, 1 comment}

_{Edit Code Review Agent Settings | Greptile}

[github-actions]

Size Change: 0 B

Total Size: 3.4 MB

ℹ️ View Unchanged

Filename	Size
frontend/dist/toolbar.js	3.4 MB

_{compressed-size-action}

[chatgpt-codex-connector]

💡 Codex Review

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[posthog-bot]

⏭️ Skipped snapshot commit because branch advanced to 9f248d9 while workflow was testing 74514ee.

The new commit will trigger its own snapshot update workflow.

If you expected this workflow to succeed: This can happen due to concurrent commits. To get a fresh workflow run, either:

• Merge master into your branch, or
• Push an empty commit: git commit --allow-empty -m 'trigger CI' && git push

[posthog-bot]

Visual regression: Storybook UI snapshots updated

Mode: UPDATE (triggered by human commit 15f0880)

Changes: 7 snapshots (7 modified, 0 added, 0 deleted)

What this means:

• Snapshots have been automatically updated to match current rendering
• Next CI run will switch to CHECK mode to verify stability
• If snapshots change again, CHECK mode will fail (indicates flapping)

Next steps:

• Review the changes to ensure they're intentional
• Approve if changes match your expectations
• If unexpected, investigate component rendering

Review snapshot changes →

[Twixes]

Merged with #41850