Have a look at a similar project of mine https://community.home-assistant.io/t/diy-interactive-photo-frame-with-pop-up-cards-music-playing-camera-feed-google-maps-etc/191397.
You don’t really need any seperate integration as everything can already be achieved within HA.
You can create a dedicated lovelace tab for this purpose alone. There are existing custom cards (for example) to display your calendars, or pretty much anything else.
*edit : I also started this project using Dakboard.
However, after putting some effort into it, I’ve figured that a lovelace tab is much more powerful, local and allows you to display not only your calendars or notes, but also other important stuff (such as camera alerts) or even allows you to play music directly within HA.
Have a look at my project for further inspiration.