ENG-7585: docs patch (+ ENG-7581)

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ENG-7585 Patches to Reflex Web Navbar + Sidebar

ENG-7581 Refine the AI Docs

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Greptile Summary

This PR implements a comprehensive documentation and navigation cleanup for the Reflex web repository, focusing primarily on the AI Builder documentation section. The changes span multiple areas:

Documentation Content Updates: The PR updates AI Builder documentation by removing 'API' from integration examples in interaction modes, updating an embedded YouTube video to showcase newer IDE features, and removing a 'Common Use Cases' section from the general app lifecycle documentation to streamline content focus.

Navigation Infrastructure Improvements: Several navigation-related changes improve consistency and user experience. The sidebar item formatting logic now properly capitalizes 'MCP' (Model Context Protocol) acronyms alongside existing acronym formatting for API, CLI, AI, and IDE. The navbar's AI Builder link now directs users to the 'best practices' page instead of 'what is reflex build', suggesting a shift toward more actionable entry points.

State Management and Routing Fixes: The PR addresses navigation state management issues by modifying how sidebar navigation works. The sidebar category function now uses a standardized JavaScript redirect pattern (href='#' with on_click events) instead of direct href navigation, ensuring proper state updates before navigation occurs. Additionally, caching was removed from the sidebar_index computed property to ensure real-time responsiveness to URL changes, fixing potential issues where the active sidebar section wouldn't update correctly during navigation.

Path Management: Hardcoded URL paths are replaced with dynamic path references from imported modules, improving maintainability and reducing the risk of broken links when routes change.

These changes collectively improve the documentation structure, fix navigation bugs, and establish more consistent patterns across the codebase while maintaining the existing functionality.

Confidence score: 4/5

• This PR is generally safe to merge with minimal risk, consisting primarily of documentation updates and navigation improvements
• Score reflects that while most changes are low-risk documentation updates, the navigation state management changes could potentially affect user experience if not properly tested
• Pay close attention to the sidebar state management changes in pcweb/components/docpage/sidebar/state.py and pcweb/components/docpage/sidebar/sidebar.py to ensure navigation works correctly across all documentation sections

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