Graceful Context7 chat widget transitions

[MarketDataApp]

Summary

• Sticky widget: Chat bubble stays on non-widget pages (e.g. /account/) only if the user has opened it at least once. If never interacted with, the bubble is cleaned up.
• Deferred switching: When navigating between SDK sections (e.g. Python → PHP) while the user has an active conversation (panel open + messages sent), the switch is deferred until the user closes the chat panel.
• Immediate switching: When the chat panel is closed or the user hasn't sent any messages, switching between SDK sections happens instantly.
• Theme fix: Dark/light mode toggle now updates widget colors in-place via shadow DOM style rewriting instead of destroying and recreating the entire widget (which previously lost conversations).

Test plan

• Navigate to /sdk/py/ → widget loads
• Navigate to /account/ without opening chat → bubble disappears
• Navigate to /sdk/py/, open chat, close it, navigate to /account/ → bubble stays (sticky)
• Navigate to /sdk/php/ with panel closed → immediate switch to PHP
• Open chat on /sdk/py/, type a message, navigate to /sdk/php/ → chat stays open with Python context
• Close the chat panel → silently switches to PHP widget
• Toggle dark/light mode while chatting → color changes without destroying conversation

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