Fix tooltip minimize flow design

[arunshenoy99]

• Always render FloatingIcon into the DOM so it appears when minimize is clicked during tooltip flow (previously only mounted if hasLaunchedFromTooltip was true at page load)
• Show legacy header (minimize + close) when in tooltip flow regardless of AI capability, replacing the "Close and show AI chat" dismiss bar
• Restore floating icon to original help-bubble.svg design with "Help" label
• Fix hover styles for help-bubble SVG (stroke/fill colors for contrast)

Proposed changes

Type of Change

Production

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Dependency update
• Refactoring / housekeeping (changes to files not directly related to functionality)

Development

• Tests
• Dependency update
• Environment update / refactoring
• Documentation Update

Visual

Checklist

• I have read the CONTRIBUTING doc
• I have viewed my change in a web-browser
• Linting and tests pass locally with my changes
• I have added tests that prove my fix is effective or that my feature works
• I have added necessary documentation (if appropriate)

Further comments

[github-actions]

Coverage: Base 35.54% → PR 35.54% (must not decrease).
✅ No decrease.

project coverage report 35.54% @ 1d6d118