Surveys: Support partial response collection

🚨 IMPORTANT

This issue is likely user-facing in the main PostHog app, see surveyVersionRequirements.ts. If you delete or close this issue, be sure to update the version requirements list there.

Summary

The posthog-flutter SDK does not support partial response collection for surveys.

Current State

• Flutter wraps the native iOS and Android SDKs for surveys
• Neither native SDK currently supports partial response collection
• This issue depends on the native SDKs implementing the feature first:
  • iOS: https://github.com/PostHog/posthog-ios/issues/447
  • Android: https://github.com/PostHog/posthog-android/issues/390

Expected Behavior

When enable_partial_responses is enabled on a survey:

1. The SDK should track responses incrementally as the user answers each question
2. When a user dismisses or abandons a survey without completing it, the partial responses should be captured
3. Events should include $survey_partially_completed: true property when responses exist but survey isn't complete
4. Question shuffling should be disabled when partial responses are enabled (responses are tracked by question ID)

Reference Implementation

See posthog-js browser: packages/browser/src/extensions/surveys/surveys-extension-utils.tsx

Tracking

This is tracked in the survey SDK feature parity issue: https://github.com/PostHog/posthog/issues/45658

This issue was generated by Claude during a Surveys SDK audit.

Start with frontend/src/scenes/surveys/surveyVersionRequirements.ts and the referenced browser implementation in packages/browser/src/extensions/surveys/surveys-extension-utils.tsx. Check the linked iOS and Android SDK issues first, since Flutter support depends on them; done means partial responses are collected and marked as specified, with question shuffling disabled when enabled.