Make text input controllable

[rebeccaalpert]

Composer AI Studio is looking for a controlled text input for the footer.

Details on their use case:

• Don’t want the example prompts to automatically be sent on click, just to add them to the prompt text box on click.
• The example prompts may need a file to be uploaded or a variable to be updated in the text box before sending.

[rebeccaalpert]

This is going to require a swap away from the current input field we are using. This is somewhat involved.

Related issue: #378.

Fixing one of these should allow us to fix the other.