Implement survey popup delay (surveyPopupDelaySeconds)

🚨 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 here.

Summary

The posthog-flutter SDK does not implement the survey popup delay (surveyPopupDelaySeconds). The field is not present in the Flutter SDK code at all.

Current State

• No surveyPopupDelaySeconds field or delay logic exists in the Flutter SDK
• The underlying native SDKs (iOS and Android) have the field in their models but do not implement the delay behavior either

Expected Behavior

When survey.appearance.surveyPopupDelaySeconds is set to a value > 0:

1. The survey popup should be delayed by that many seconds before being shown
2. Surveys should be sorted by their delay value (shorter delays first)

Dependencies

This depends on either:

• The Flutter SDK implementing the delay itself in its survey rendering code
• Or the native SDKs implementing it (iOS needs rendering delay, Android needs to expose on display model)

Reference Implementation

See posthog-js browser: packages/browser/src/extensions/surveys.tsx — _handlePopover() method which uses setTimeout for the delay.

Tracking

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

This issue was generated by Claude using the /survey-sdk-audit skill.

Start by reading the Flutter SDK survey rendering code and compare it with packages/browser/src/extensions/surveys.tsx, especially the _handlePopover() method. Check surveyVersionRequirements.ts and the linked feature-parity issue for scope, then implement the delay and ordering behavior so surveys wait for surveyPopupDelaySeconds and shorter delays appear first.