add feedback widget with posthog

[HarshCasper]

This PR:

• Implements a docs feedback system using PostHog Surveys
• Adds an API-based survey capture with "Was this helpful?" yes/no flow and optional text feedback
• Added contextual follow-up questions: positive feedback shows "What did you like?" options, negative shows "What went wrong?" options
• Styled widget for both light/dark modes with compact UI, radio buttons, and success state

[cloudflare-workers-and-pages]

Deploying localstack-docs with    Cloudflare Pages

Latest commit:	5244101
Status:	✅  Deploy successful!
Preview URL:	https://cd298726.localstack-docs.pages.dev
Branch Preview URL:	https://feedback-widget.localstack-docs.pages.dev

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[remotesynth]

As noted, please adjust the colors of the line and text to match.

[quetzalliwrites]

It works amazing! The only thing I want to change is placement.

Placing the feedback widget at the bottom of a docs page is a best practice. This strategic placement ensures users have consumed the content BEFORE being asked to evaluate it, leading to more informed, context-aware insights.

Contextual Relevance (After Reading)

Users are more likely to provide valuable feedback (such as identifying, for instance, that a code sample didn't work) AFTER they have finished reading a tutorial. Placing it at the bottom aligns with the natural end of a user's task.

Also...There's no need for a line to separate this widget, I consider that clutter and would remove.

(some screenshot examples below)

[quetzalliwrites]

Just 2 things:

• fix color text (perhaps ask Lazar to confirm which one to use for this?)
• update widget placement to bottom of doc page