Figured it out. For those interested, I needed to add the type 'associatedInputs' to the data object. Updated Formula works as intended.
{
type: "AdaptiveCard",
actions: [
{
type: "Action.Submit",
title: "Contact Us",
data: {
topicTrigger: "Topic.ContactUs",
text: "Contact Us",
associatedInputs: "none"
}
}
],
'$schema': "https://adaptivecards.io/schemas/adaptive-card.json",
version: "1.5"
}