You would need to also add a name to the input/1. As we see in the component it is expecting @name to be set, so we can pass it in like so:
<.input name="first_name" field={{f, :first_name}} type="text" label="First Name" />
<.input name="email" field={{f, :email}} type="email" label="Email" phx-debounce="blur" />
