Hi Jennie,
so you are not able to activate the Playfair Display font with the Adobe Fonts Service.
What's your version of InDesign and operating system?
Are you on a Mac with the new M1 chip?
The first thing what I would try:
[1] Log out of the Creative Cloud Desktop App.
[2] Restart your machine.
[3] Log in with the Creative Cloud Desktop App.
[4] Go to the Adobe Fonts website and activate the Playfair Display font there:
https://fonts.adobe.com/fonts/playfair
[5] Startup InDesign to see if InDesign can access the font
Maybe you can also find an answer at the Adobe Fonts User Forum:
https://community.adobe.com/t5/adobe-fonts/ct-p/ct-fonts?page=1&sort=latest_replies&tabid=all
Regards,
Uwe Laubender
( ACP )