Is there an "easy" way to show Teams cards on the intranet home page?

I don't think there is an out-of-the-box or even an easy way to do this.

If this is a make-or-break functionality and development is an option, probably this would be my approach/architecture:

1. Create an Azure Function that runs on a timer and uses List channel messages and Get channel messages delta to fetch the latest messages, and filter on "Praise Bot" (there is no change notification/webhook support). Downside: this would be limited to a specific channel, you can't get all messages for a user/bot through Microsoft Graph.

2. For a Group connected site: use the Connector webpart and let the Function post as a Adaptive Card

3. For a Classic/Non-group connected site/Communication site: create an SPFx web part that can accept this data and present it

It's not the best experience...