I’d suggest doing this with a custom state of type Text. Set the Input’s default value to that custom state. When the ‘use suggestion’ button is clicked, set the custom state’s value to This Cell’s text (or similar).
You’re correct about that! I often forget Bubble has different naming conventions for different element types. In this case I would use the Input’s Initial Content.
This will work until the user enters data into the input field; if this is a possibility you wish to avoid, you can add a step of ‘Reset Group’ prior to the set custom state, which should clear the group’s inputs and therefore be receptive to an Initial Content’s value changing, and therefore appearing in the input’s ‘Initial Content’