[AIChat] - Enter Prompt Input UI

[Brandon-T]

Feature Overview

• A user needs a place to enter their prompt that brings up the keyboard, the ability to dismiss the keyboard, and the ability to enter the prompt with voice-search

Implementation Details

• Implement the input field
• Implement the ability to dismiss the keyboard on swipe down
• Implement the ability to enter a prompt via voice-search
• Implement the "send" button change when the text field is not empty

[kjozwiak]

As per brave/brave-browser#36585 (comment) & https://bravesoftware.slack.com/archives/C04KPE0BUDU/p1709872123838319?thread_ts=1709830872.231289&cid=C04KPE0BUDU, going to close this one off as QA/No and release-notes/exclude as we'll use brave/brave-browser#36585 as a guide/main issue to run through Leo via 1.63.x.