Refactor FloatingInputView and FloatingInput into single reusable component

[huypham37]

Context

Currently there are two similar input components:

• FloatingInputView in FloatingInputView.swift (empty chat home with sparkles icon)
• FloatingInput in ReportView.swift (bottom of conversation)

Both share similar logic but are duplicated.

Problem

• Duplicate code for input handling
• Changes need to be applied in two places (e.g., note indicator was added to both)
• Inconsistent styling possible

Proposal

Refactor into single flexible component:

• Optional icon/branding for home screen mode
• Shared input logic and styling
• Single source of truth for note indicator, send button, etc.

Acceptance Criteria

• Single reusable input component
• Works in both empty state and conversation views
• No duplicate code