Answer
Controls near the bottom stay visible above the composer as they appear, including while you read older messages. If the controls already fit, your reading position stays still. Your scrolling or navigation takes priority over an automatic adjustment, and reduced motion is respected.
New chats and page refreshes open at the newest message's content bottom. Reopening a chat during the same app or page session remembers your reading position. A refresh clears that temporary memory. Opening a link to a specific message still goes to that message.