Create chat page

The chat page should show a typical chat like you see on many modern apps:
- Text field at the bottom
- Messages from you on the right
- Messages from the other party on the left

This issue is just about implementing the design, not showing new messages as they arrive, so start off just by hard-coding a fixed list of messages and displaying those on the screen. We will implement adding new messages to the view later, but it's a separate issue.

The issue names no files, tests, or entry points. Start by locating the existing page structure and UI patterns, then implement a chat view with a fixed message list, a bottom text field, and distinct left/right message alignment. Done means the static chat layout matches the described design without implementing live message updates.

Written by the indexing model from the issue text.