docs: document addSessionProperties method

[ccschmitz-launchdarkly]

Summary

This PR adds user-facing documentation for the addSessionProperties method that was implemented in PR #247. The method allows developers to add custom session-level properties that are searchable in LaunchDarkly without creating timeline track events.

Key additions:

• New "API Reference" section in the Session Replay SDK README
• Usage example showing how to call LDRecord.addSessionProperties()
• Clear explanation of when and why to use session properties vs track events

How did you test this change?

• Verified documentation formatting with yarn format:all
• Reviewed existing JSDoc comments and e2e test usage for accuracy
• Confirmed the API surface matches what's exposed in the @launchdarkly/session-replay package

Are there any deployment considerations?

No deployment considerations - this is documentation only and will be published with the next package release.

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Link to Devin run: https://app.devin.ai/sessions/c37a8e09a1eb45498053821a57f0e051
Requested by: @ccschmitz-launchdarkly

Review Checklist

Please verify:

• The documented API matches the actual implementation in PR feat: add addSessionProperties to RecordSDK #247
• The TypeScript examples are syntactically correct
• The explanation accurately describes the behavior (searchable properties, no timeline events)
• The documentation placement and style is consistent with existing patterns

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Note

Adds an API Reference section documenting LDRecord.addSessionProperties with a usage example and explanation of searchable session properties without creating track events.

• Docs (Session Replay README):
  • API Reference: Adds "Adding Session Properties" section.
    • Documents LDRecord.addSessionProperties() with TypeScript example.
    • Clarifies session-level properties are searchable in LaunchDarkly and do not create timeline track events.

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[devin-ai-integration]

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[devin-ai-integration]

Closing this PR as the documentation should be added to the ld-docs-private repository, not the SDK repository. Opening a new PR in the correct repo.